solid geometry formulas pdf

Euclidean Geometry refers to the study of plane and solid figures on the basis of axioms (a statement or proposition) and theorems. 0000001114 00000 n The study of angles in a unit circle and that of a triangle forms the stepping stone of trigonometry. The distance formula, the section formula, midpoint formula, the centroid of a triangle, the area of the triangle formed by three given points, and the area of the quadrilateral formed by four points are determined using the known coordinates in the cartesian coordinate system. Imagine a Coca-Cola Can for a good example! FOUNDATION . For further or more advanced geometric formulas and properties, consult with a SLAC counselor. Area of a triangle Area of a parallelogram Area of a trapezoid Area of a circle Volume of a rectangular solid Volume of a cube Volume of a sphere Volume of a cylinder Volume of a square based pyramid Volume of a right . Solution: In geometry, we know that similar triangles are proportional. d is the diameter of the circle. Once yousubscribetoEdge 2021,youll get access to all the courses* available at the platform. Cooking is therapeutic! 2 flare services (the top and the bottom) Cube : A cube is solid with six square sides. This line on a sphere is an arc and is called the great circle. Shapes in The properties of plane shapes help us identify and classify them. Online Classes, www.takshilalearning.com call 8800999284 shapes examples] Circumference of a circle =2r Where, r is the radius of the circle. When two straight lines or rays intersect at a point, they form an angle. Complete Geometry Short Course Features. Cylinder r2 Do not sell or share my personal information. Ltd. Latest Pattern SSC CGL Tier 2 Mock Test Attempt Now, Latest Pattern SSC CHSL Tier 1 & Tier 2 Mock Tests Attempt Now, Geometry Formulas PDF Free Ebook Download Here, Enroll For Complete Geometry Short Course, Oliveboard Edge 2021 Online Exam Preparation Platform, Top 50 SSC CGL Previous Year GK Questions Part 1: Download Full Pdf Here, The Hindu Editorial Daily Vocabulary Words 27 January 2020. are also called solids. Measurement in geometry ascertains the calculation of length or distance, the area occupied by a flat shape, and the volume occupied by the solid objects. 0000000834 00000 n Solid Formula List (solid Answer: The vertex of the given parabola is at (-1, 3). 230 0 obj <> endobj Similarly, solid shapes such as tables, chairs, notepads, or pens are all around us. mathematical olympiads 1997 1998 problems solutions from around the world maa problem book 225p b002kypabi, Modeling of Curves and Surfaces with MATLAB, Compiled and Solved Problems in Geometry and Trigonometry, Titu Andreescu_ Zuming Feng - Mathematical olympiads, A $1 Problem - Mathematical Association of America, Project Gutenberg's First Six Books of the Elements of Euclid, MECHANICAL ENGINEERING FORMULAS AND REVIEW MANUAL, Inequalities proposed in "Crux Mathematicorum", YEAR 12 BILL PENDER CAMBRIDGE Enhanced 3 Unit Extension 1. All sides are perpendicular to each other or are at 90-degree angles. The plane geometric shapes are two-dimensional shapes or flat shapes. If A = B and C = D, then A + C = B + D. If equals are subtracted, the remainders are equal. Plane and Solid Geometry Formulas Prepared by: RTFVerterra hexagon, and a regular hexagonal prism has a base of a regular hexagon. The 5th Euclidean postulate on parallel lines is not validated by the hyperbolic geometry. endobj Two types of geometry are plane geometry and solid geometry. endstream endobj 66 0 obj<>stream Identifying and plotting points will be a building block of visualizing the geometric objects on the coordinate plane. U \iCU5#6>~kn\$^$ >N-0U ofT,~q=fQf"96 @-ug|NZ0P 2. Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh. However, since we know that a square has equal sides and this shape is made of 6 The skew lines are the lines in space that are neither parallel nor intersecting, and they lie in different planes. 0u\5fX m"7>[BUiG1/d&m"$Y:?D.UG+k3)D4XN)X7_~&+4.4N+KSDyrTteJQHK9diMZ1 faI1c!*0lSX aXv{F&MFxrM-ML[|~$)PK]ftf&yM*}wXYtBE%SSH+iq>Wl6W;oBSM}}!eFS1H.\g`x@Kv}O5E{}]lZBYUK(./dNcDZ`,5xpy3P08 5B9Gs@G4 2f>OA=?;0k(Id6-"e7r95Zx'QJH~%3u3JF0qa]+#X!P?j"]/%ox`wI} "7@X 4.7 Applications to geometry 68 4.8 Vector equations 72 5 Spherical geometry 74 5.1 Spherical distance 74 5.2 Spherical trigonometry 75 5.3 Area on the sphere 77 5.4 Euler's formula 79 5.5 Regular polyhedra 83 5.6 General polyhedra 85 6 Quaternions and isometries 89 6.1 Isometries of Euclidean space 89 6.2 Quaternions 95 6.3 Reections and . Solution: In 3-dimensional geometry, if a straight line makes angles , and with the x-axis, y-axis, and z-axis respectively then cos, cos, cos are called the direction cosines of a line. 0000000016 00000 n Geometric Formulas. Cylinders . 566 26 pdfcoffee.com plane-and-solid-geometry-formulas-pdf-free, MATH 103 Plane and Solid Mensuration Formulas, 2013 - 2023 studylib.net all other trademarks and copyrights are the property of their respective owners. The sum of angles in a triangle is less than 180. E.g., cuboid, cone, cylinder, sphere, cube, pyramid. Euclidean geometry involves the study of geometry in a plane. examples[/caption] Solid Mensuration Formulas | PDF | Triangle | Circle - Scribd . 7. 566 0 obj <> endobj Quiz 3: 5 questions Practice what you've learned, and level up on the above skills. The product of length and width is the area of the rectangle. For l, m, and n, l2 + m2 + n2 = 1, direction cosines of a line joining the points P(\(x_1, y_1, z_1\)) and Q(\(x_2, y_2, z_2\)) are given as :\(\dfrac{x_2-x_1}{PQ}, \dfrac{y_2-y_1}{PQ}, \dfrac{z_2-z_1}{PQ}\), where PQ = \(\sqrt{((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\), The directional ratios of a line are the numbers that are proportional to the direct cosines of the line. Thus it has its practical applications in our day-to-day life. Save. A few of Euclid's axioms in geometry that are universally accepted are: Spherical geometry and hyperbolic geometry are the two non-Euclidean geometries. Solids: Definition Feel free to send suggestions. Maths[/caption] 1 vertex 2 0 obj 0 flat surfaces Download. Solid mensuration formulas - [PDF Document] Plane and solid geometry formulas pdf. Formulas Thus Euclidean geometry is used in art and architecture, computer science, astronomy, and other fields of mathematics. 0000021417 00000 n Figures with three Perimeter: 4. <>>> PDF Plane Figure Geometry Formulas - roguecc.edu 4. 0000012763 00000 n %PDF-1.3 % 0000006992 00000 n Three-dimensional shapes - Such shapes have three dimensions, i.e., length, breadth, c 2006 Kiran S. Kedlaya. The construction of angles and lines is an intricate component of geometry. Lines may or not intersect. 0000010536 00000 n Prism Solution. Geometry Points, Lines & Planes Collinear points are points that lie on the same line. A two-dimensional surface extending infinitely in both directions forms the plane. It is a 3-dimensional figure with length, breadth, Some attributes of solid geometric shapes are as follows: endstream endobj 231 0 obj <>/Metadata 7 0 R/Outlines 11 0 R/PageLayout/OneColumn/Pages 228 0 R/StructTreeRoot 22 0 R/Type/Catalog>> endobj 232 0 obj <>/Font<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 233 0 obj <>stream 1. xbba`b``3 1x8@ ; | Furthermore, this Academia.edu no longer supports Internet Explorer. . With Cuemath, you will learn visually and be surprised by the outcomes. Solution: In 3-dimensional geometry, if a straight line makes angles , and with the x-axis, y-axis, and z-axis respectively then cos, cos, cos are called the direction cosines of a line. Would you agree that a pyramid is a 3-dimensional form of a triangle? B Incenter of the triangle r= Sector of a circle Diagonal, d = a 2 + b 2 A Perimeter, P = n x n2 180 Interior angle = n Exterior angle = 360 / n Circumference = 2 r = D 2 Area, A = r2 = D 4 ( s a) ( s b) ( s c ) ( s d) "For any cyclic quadrilateral, the product of the diagonals equals the sum of the . 4. 22. 0000000016 00000 n 2. What is the vertex of the given parabola? There are different types of solid figures like a cylinder, cube, sphere, cone, cuboids, prism, pyramids, and so on and these figures acquire some space. Solids Shapes (Solid geometry) in Maths & their types and Its properties are as follows: www.takshilalearning.com call 8800999284 Solid Shapes in Maths[/caption] Solids Shapes (Solid geometry) in Maths & their types and Formulas Solids or three-dimensional forms are three-dimensional shapes with three (or more) dimensions in geometry. As Im doing. Solid geometry formulas. Cavalieri's principle and dissection methods. This complete e-book will help you in understanding the Geometry Formulas much more ease and convenience. some solid examples and attributes of solid forms. Calculate the surface area and volume of a cube where a side is 6 cm. At,X3W2"]tWw/55[oYeocg$2Ey3;6JwJ[. The z-axis makes 90, 90, and 0 with x, y, and z axes respectively. By using our site, you agree to our collection of information through the use of cookies. Shapes in Maths[/caption] Plane and Solid Geometry Formulas Prepared by: RTFVerterra Solids: Types Oliveboard Live Courses & Mock Test Series, SSC CGL 2023SSC CGL Notification 2023SSC CGL Exam DateSSC CGL Syllabus and Exam PatternSSC CGL Admit CardSSC CGL Previous Year PapersSSC CGL SalarySSC CGL Cut OffSSC CGL ResultSSC CGL Eligibility CriteriaSSC CGL Selection Process. Find the length of BC if AD = 7 units, DB = 3 units, AE = 4 units and DE = 7 units. Solid, www.takshilalearning.com call 8800999284 C is the circumference of the circle. Thus, a hexagonal prism is one whose base is a, Do not sell or share my personal information. RBI Grade B Selection Process 2023, Check Phase 1,2 & Interview!! Prepare CBSE Class 7 & Class 8 Maths with our Online Tuition Classes and Interactive Live Given that side, a = 8 cm Find the volume of a cube with side lengths of 6 meters. Example 6.3. meet. Circle Area of a Circle = r. trailer The five basic postulates are meant to be the fundamentals of geometry learned in the formative years. 0000005449 00000 n Calculate the total surface area of a cuboid with dimensions of 6 cm 5 cm 9 cm. 1 curved face examples[/caption] <> = 6*8*8 = 384 cm2 0000003719 00000 n [Arithmetic, Plane Geometry, and Space Geometry]. Rectangular Solids (Boxes) Cubes . Here the parabola opens up, so the axis of symmetry is vertical. Distance Formula: Midpoint Formula Regular: all angles are and all sides are . 4. ] 3. endobj His book 'Elements' is the most influential work in maths serves as the fundamentals of geometry. \vec b_2}{|\vec b_1| |\vec b_2|}\)|. There are many postulates and theorems applied by the Greek mathematician Euclid, who is often referred to as the Father of Geometry. Mention different types of solid shapes(solid shapes names). Answer: The direction cosines of the z-axis are 0,0,1. 6 faces There are 5 basic postulates of Euclidean Geometry that define geometrical figures. SA = B + rS. Now that we know about the properties of all these solids, lets also make a note of all its 8 vertices Quadrilaterals are polygons with four sides and four vertices. Geometry Formulas PDF - Free Download - Oliveboard The three dimensions that are taken into consideration are length, width, and height. Find the volume of the sphere of the radius of 3 cm. Freely redistributable. Circle inscribed in a triangle (Incircle) Parallelogram Number of diagonals, D. The diagonal of a polygon is the line A circle is inscribed in a triangle if it is tangent to. Teaching geometry is not an easy task that can be done with a textbook and drawing some shapes on the board. point. It might be The things that are equal to the same things are equal to one another. 1. 0000005011 00000 n Similar polygons of different areas don't exist. Plane and Solid Geometry by d1 The number of diagonals is given by: B. d2 Incenter of. Chooseany course, any time,whenever you like. %PDF-1.5 5. 0000002043 00000 n Academia.edu uses cookies to personalize content, tailor ads and improve the user experience. Cube. 0000002949 00000 n 6.3: Volume of Geometric Solids - Mathematics LibreTexts endobj %PDF-1.4 % 0000011572 00000 n You can add this document to your study collection(s), You can add this document to your saved list. Cuboids total surface area = 2 (lb + bh + hl) Volume, V, (using volume for a cylinder ): V 1 = r 12 h for the volume enclosed by C 1. Is the category for this document correct. If a straight line makes angles , and with the x-axis, y-axis, and z-axis respectively then cos, cos, cos are called the direction cosines of a line. <> 2. In the example below, point A is defined as (4,3) and Point B is defined as (-3,1). $rBf9[9Ox~pH9k\eoR.6vSdOhX^C3c! 0000000556 00000 n Imagine a shoebox or a wooden box for a good example! If l, m, n are the direction cosines, and a,b c are the direction ratios, then, m = \(\dfrac{b}{\sqrt{a^2+b^2+c^2}}\) and. % I enjoy creating SEO-friendly, information-rich marketing content. Its properties are as follows: Plane geometry deals with two-dimensional shapes and planes (x-axis and y-axis), while solid geometry deals with three-dimensional objects and 3D planes. Solid Mensuration Formulas - Free download as PDF File (.pdf), Text File (.txt) or read online for free. In this e-book, you will find all the relevant inputs that are needed to tame this part of Quantitative aptitude. (Formula list for Solid Shapes in Maths) shapes Example: 3 Find the direction cosines of the z-axis. All the visually and spatially related concepts are categorized under geometry. Geometric Shapes: Some Attributes Two-dimensional shapes - Such shapes have two dimensions of length and breadth. The following figure is a convex, Polygons are classified according to the number, of sides. The three-dimensional geometry discusses the geometry of shapes in 3D space in the cartesian planes. 3 0 obj A cube and a cuboid are distinguished by the fact that a cube has six identical square-shaped LW is the formula used in geometry to find the area of a rectangle. Substituting the values, cuboids surface area = 2 (6*5 + 5*9 + 6*9) = 258 cm2 2. The plural form of a vertex is vertices. 3|Dc5t\3ZmBh#"0~uPU*:J# TQ38zc^ Its properties are as follows: You can get the Geometry Formula for Classes 12, 11, 10, 9, 8 from our page. 4. 0000002702 00000 n Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height. A triangle is a closed figure with three sides and three vertices. DOCX, PDF, TXT or read online from Scribd, 71% found this document useful, Mark this document as useful, 29% found this document not useful, Mark this document as not useful, Save Plane and Solid Geometry Formulas For Later. Chapter 1 Basic Geometry An intersection of geometric shapes is the set of points they share in common. Course: Bachelor of Science in Civil Engineering (BSCE) 585 Documents. Geometry Formulas for Class 12, 11, 10, 9, 8 - Learn Cram hWmo6+xX A line is a uni-dimensional unit that refers to a set of points that extends in two opposite directions and the line is said to be the intersection of two planes. Start preparing for it whenever you want. wx-~$-9r0(X80A2,CcJh3fDd?,0JR+&Lh:LJZTIIBTwQ1jyO/]fY}yf\,$UCI7PO'WEm'itr=VLI9^/'Y*dDgjnIo? PDF Geometric Formulas - cgc.edu NABARD Grade A Notification 2023, Complete Information, Exam Date & More! What is Geometry? Plane & Solid Geometry | Formulas & Examples - BYJU'S DEVELOPMENT . An Intro to Geometry By Kiran S. Kedlaya. passes through the vertices of the triangle. Sphere PDF Geometry Formulas List Download PDF - Plane And Solid Geometry Formulas [34m2mrr3epn6] Geometric Shapes and Formulas in Solid Geometry - CalculatorSoup Cube A triangle has three, The area under this condition can also be, solved by finding one angle using cosine law, Circle circumscribed about a quadrilateral, solved by finding one side using sine law and, any cyclic quadrilateral, the product of the, diagonals equals the sum of the products of the, There are two basic types of polygons, a convex, and a concave polygon. 0 3. dimensionslength, breadth, and heightare also known as solid forms. and height. (PDF) Plane and Solid Geometry Formulas Prepared by: RTFVerterra ASIAN interior angles are called equiangular polygons. 0 Depending on the inner curvature of the curved surface, the planar triangle has the sum of the angles lesser than 180. trailer endstream endobj 591 0 obj<>/W[1 1 1]/Type/XRef/Index[23 543]>>stream Students will develop and explain formulas related to circles and the volume of solid figures and use the formulas to solve problems. Eligibility for RBI Grade B 2023, Attempts, Educational Qualification, Age Here!! These are the two types of geometry. 1. Quantitative aptitude is an integral part of almost all the competitive examinations. 4r2 The five platonic solids and the polyhedrons have interesting properties in Euclidean space. Students can Download Geometric Formulas Cheat Sheet PDF for free of cost. endstream endobj startxref Solids Shapes _Solid geometry_ in Maths & their types and Formulas.pdf A = A 1 - A 2 = ( r 12 - r 22) for the area of the solid cross section of the tube, the end, an annulus . Substituting the values, spheres volume = 4/3 * 22/7 * 3 * 3 * 3 = 112.75 cm3 In most circumstances, Now cubes surface area = 6a2 Opposite faces, as well as opposite edges, are equal. Where, l is the side length n is the number of sides 3.19. equiangular are called regular polygons. Mensuration Formulas For 2D Shapes Hyperbolic geometry illustrates three key points that differ from Euclidean geometry. endobj Non-Euclidean geometry differs in its postulates on the nature of the parallel lines and the angles in the planar space, as validated by Euclidean geometry. Example: 3 Find the direction cosines of the z-axis. 1 0 obj COLLEGE . 0000001598 00000 n Type: PDF. square, rectangular, or any other polygon. 0000000831 00000 n examples[/caption] stream Higher-dimensional shapes: Such shapes have more than three dimensions, and we PDF FORMULAS FOR PERIMETER, AREA, SURFACE, VOLUME - austincc.edu 0000001281 00000 n The equation of a straight line passing through a point, or two points, the angle between two straight lines are computed easily using the analytical geometry as they are generalized using formulas. 2. '};KL7:;I;u/~g` #% fg'|_o4QWXV[H)G3s^g l%: 0000001041 00000 n 0000000912 00000 n Cylinder Euclidean geometry considers the study of points, lines, angles, and similarity and congruence in shapes, their patterns, and their transformations. 0000008190 00000 n University: Technological University of the Philippines. +c8{w~'$ In analytical geometry, the curves are represented as algebraic equations, and this gives a deeper understanding of algebraic equations through visual representations. How to Prepare for RBI Grade B Exam, Study Plan, Preparation Strategy for Phase 1 & Phase 2. Subscribe Now and Get 50% Off on Oliveboard EDGE 2020 Subscription. 0000004659 00000 n 0000003215 00000 n JustDo it Your Way! Analytical geometry is popularly known as coordinate geometry is a branch of geometry where the position of any given point on a plane is defined with the help of an ordered pair of numbers, or coordinates using the rectangular Cartesian coordinate system. three faces join at a single vertex. 1. Every point in the space is denoted by 3 coordinates, represented as an ordered triple (x, y,z) of real numbers. %%EOF startxref Three dimensional forms, often known as solids, are shapes that inhabit space Figures with three dimensionslength, breadth, and heightare also known as solid forms Cubes, cuboids, prisms, cone, cylinder, and sphere are some examples and types of Solid shapes, Countdown Class 7th Mathematics Chapter 19 Solution, Triangles What are the properties of an Isosceles Triangle.pdf. stream Cuboid: A cuboid, also known as a rectangular prism, is a solid form of two-dimensional On the other hand, This Free PDF Notes (maths mensuration formula) and geometry formulas in hindi is important for various Sarkari exams like UPSC, IAS, RAS, UPPSC, MPPSC, BPSC, SSC CGL, CHSL, CPO, Geometry Formula Sheet Notes For State PSC, CTET . 2023 All Right Reserved Oliveboard Pvt. In this e-book, you will find all the relevant inputs that are needed to . RBI Grade B Previous Year Papers, Download Phase 1 & 2 Past Year Paper PDFs! 4 0 obj geometry cheat sheet.pdf - Google Docs 2 0 obj . SA = 2B + 2rh. Where do you get all formula of Geometry? Angles are usually measured in degrees. rectangular sides. Planes are used in every area of geometry and graph theory. Mensuration in geometry is applied to the computation of perimeter, area, capacity, surface areas, and volumes of geometric figures. A line has no endpoints. Add up all areas. s s s l w h 3V = s V = l w h Surface Area = 2(l w) + 2(l h) + 2(w h) Prism . x][o~7.q\imk{c95_f\I"ifp!Xon>/.6zy:>[}/wfuWq}>CRvE Sphere: A sphere is a solid that is completely spherical in form. Measurement of Three Dimensional Figures _Module and test questions. FAQs (Frequently Asked Questions) 1 curved surface Mensuration Maths Formulas for 2D and 3D Shapes (With PDF) - BYJU'S }]m|Iu_!^` [x^Ty1sh,f` __3:vJDncc&WQa_*F%W%! 0000013887 00000 n 6&,2[tyi~SGXaDPiP!YFbRLj pa -`-^f f!,)&M*/(Qz!a3s %B~ab4; U6- have similar structures, there are some differences in faces, diagonals, and edge length. Tacloban City . 0000001739 00000 n Solid shapes in geometry are three-dimensional in nature. There are three types of geometry: We study Euclidean geometry to understand the fundamentals of geometry. This will help you prepare for various exams like SSC CPO, SBI Clerk, RBI Assistant, IBPS Clerk , RBI Grade B , IBPS PO. <> Its very important for us! 56 0 obj <> endobj Shape Solid geometry studies the characteristics, volume, and surface area of three- % Substituting the values, cubes volume = 83 1. www.takshilalearning.com call 8800999284 However, the cube and the cuboid In general, the most common formulas in mensuration involve surface area and volumes of 2D and 3D figures. <<524DE98A493DEC4B894CD5457D15604D>]>> 20+ Geometry Books for Free! [PDF] - InfoBooks.org Its properties are as follows: Let us now turn our attention to the study of geometrical solids. 0 edges Info More info. Sphere (4/3)r3 approach can simplify how we understand the properties of such solids. h r(r + l) uPz{7OYh]ph,aAvcB"6}CCWc**"L-@3`~v<>Ki{l. in geometry. It then helps in building all other concepts in geometry that are based on these basic concepts. hb```i eap`9xG|S%@$D!';88? These help us recognize the angle-side relationships in triangles. In solid geometry, 3d shapes such as a cube, cuboid, cone, etc. Some of the teaching-learning activities are listed below: Geometry is the branch in mathematics that is further divided into various sub-branches that are given in the list below: The basics of geometry are the proper understanding of points, lines, and planes. Density. Three-dimensional forms, often known as solids, are shapes that inhabit space. An Intro to Geometry By Kiran S. Kedlaya. surface. 1 edge e-^u:|xp 1 0 obj Here are SA = 4r2. 8H7Qr(ZR;j+Czp^$ENr#,aHCbwJ{b3@/8,p')udYWGGdYr|rQ,:oe1 G(ap*O":QZS `O^r,]=.GmfpuhNd A straight line segment may be drawn from any given point to any other. hbbd``b`$ 6jIhX5$ x The following are some names of, polygons in parallel planes and whose sides are. f?s.g\om5ON |jvzNWFtrW9M0 The nets of the plane shapes can be folded into solids. This geometry finds its application in topology. PDF Geometry Formulas and Shape - tcc.fl.edu PDF Math Handbook of Formulas, Processes and Tricks - MathGuy.US Never Mine, hes the only autor. name) The fundamental concepts of Euclidean geometry include Points and Lines, Euclids Axioms and Postulates, Geometrical Proof, and Euclids Fifth Postulate. BASIC GEOMETRIC FORMULAS AND PROPERTIES This handout is intended as a review of basic geometric formulas and properties. Looking at the graph we know that the axis of symmetry is the y-axis, which is x = -1. 2. UQhsncwtvwfwqspq\t*uq Vector equation of the line passing through a point with the position vector \(\vec a\) and parallel to vector \(\vec b\) is \(\vec r = \vec a+ \lambda \vec b\), Cartesian equation of the line passing through the point (\(x_1, y_1, z_1\)) and direction cosines l, m, n is \(\dfrac{x -x_1}{l} =\dfrac{y -y_1}{m}= \dfrac{z -z_1}{n}\), Vector equation of the line passing through two points with the position vectors \(\vec a\) and \(\vec b\) is \(\vec r = \vec a+ \lambda(\vec b -\vec a)\), Cartesian equation of the line passing through the points (\(x_1, y_1, z_1\)) and (\(x_2, y_2, z_2\)) is \(\dfrac{x -x_1}{x_2 -x_1} =\dfrac{y -y_1}{y_2 -y_1}= \dfrac{z -z_1}{z_2 -z_1}\).

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