A plane meets the coordinate axes in A,B,C .If the centroid of AABC is (a,b,c).Show that the equation of the plane is +? + = = 3 b

Q: Consider three points in three-dimensional space: ?=(11,2,−3),?=(2,−3,11),?=(−3,11,2) Let ? be the…

A: Let us consider the given points be To find the equation of plane containing the points A, B and C.…

Q: Find the coordinates of the centroid of the triangle with the given vertices. X(1, 4), Y(7, 2), Z(2,…

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Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

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Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (a, 0), (a /…

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A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Consider the points A(3, –3, 3), B(4, –5, 0), C(-3, –4, 0), and D(6, 2, –6). Find the volume of the…

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Q: Some crystals have rhombohedral structures. A rhombohe- dron is a parallelepiped in which all of the…

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Q: A quadrilateral has the following vertices given: P1(1,4),P2(3,4),P3(3,6),P4(1,6).the coordinates…

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Q: Points A and B are known to lie in a plane. a. What can you say about AB? b. State the postulate…

A: Solution: Consider the given that A and B are two points in any plane  (a) According to the…

Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the…

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Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).…

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Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c  And, the plane is, Ax+By+cZ+D=0

Q: Use the figure at the right for Exercises 8-11. 8. What are two other ways to name EF? 9. What are…

A: In the question we need to name line and plane.

Q: Answer the question in the picture.

A: Concept:

Q: Find the Cartesian equation of the plane containing the points A(4,0,4), B(1,5.5) and C(-1,-1.2).…

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Q: Which of the shapes below can make a regular tessellation of the plane?

A: there are only three regular polygons for tessellation and they are equilateral triangle, square and…

Q: Consider the points A(1,-1, 4), B(2, –3, 2), C(-1,-2, 2), and D(4,3, -6). (a) Find the volume of the…

A: Let's find.

Q: Determine whether the planes are parallel, orthogonal, or neither. 3x 15y 3z = 3 3x 15y 3z = -4 - -…

A: The given planes are 3x-15y-3z=3 and 3x-15y-3z=-4

Q: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer.…

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Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

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Q: The corners of a quadrilateral are (4, 0), (12, 4), (10, 8), and (4, 4). How far is its centroid…

A: Given data is: The corner points of a quadrilateral are 4,0, 12,4, 10,8, and 4,4 To find how far is…

Q: 2-) Calculate the distance d of the pont P(-1,1,-2) through the throe points the plane pu sing from…

A: The distance d of the point p=(-1,1,-2) from the plane passing through the points A(1,-1,1)  ,…

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, z…

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Q: O Find an equahion for the plane throught (1,-,3) parallel to the plane 3xy+Z=7

A: According to q&a guidelines I can do only 1question

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (-1, 0), (1, 0), (0,…

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Q: Consider a, B = 0. A possible graphical representation for the equation plane ax = By is: A) B)

A: Given  α,β≠0.we have to find the graphical representation for the equation plane.αx=βy

Q: A plane meets the coordinate axes in A, B, C. If the centroid of AABC is (a, b, c). Show that the…

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Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A: Let plane contain point x,y,z.

Q: If A, B, C, and D are collinear, then they lie in the same plane. A, B, C, and D lie in the same…

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Q: Consider the points A(2, –3, 3), B(3, -5, 0), C(-3, –-4,0), and D(3,3, -6). | (a) Find the volume of…

A: Note: According to our answering guidelines we have to answer only one question if multiple are…

Q: The general equation of the plane that containsteh points (1,0,3),(-1,1,-3)and the origin is of the…

A: Given general equation of plane is

Q: Find the centroid of the triangle formed by joining the points A (3, 2), B (-1, 4), and C (5, -3).…

A: Explained below

Q: Consider the points A(3, -3, 2), B(6,-5,0), C(-1, -4,0), and D(6,3, –4). (a) Find the volume of the…

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Q: Consider the rhombus shown. B A Given: Rhombus ABCD with diagonals AC and BD intersecting at point…

A: Given:- Rhombus ABCD with diagonals intersecting at a point E.

Q: Consider the points A(1, -1,4), B(2,-3, 2), C(-1, -2, 2), and D(4, 3, –6). (a) Find the volume of…

A: The answer is shown in step 2.

Q: The two vertices of a triangle are (3, –6) and (9, -4). Find the ordinate of the third vertex so…

A: Dear Learner,We Expert are following bartleby expert guidelines to answer the question,so we can…

Q: The centroid of a triangle lies at the intersection of the triangle's medians, because it lies…

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Q: Consider the plane shown in the following figure: Let 4, b, c, d 40. A general equation…

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Q: Find the centroid of the triangle whose vertices are  O(0,0) , A(4,0) and B(0,6)

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Q: Given the three points A(2, 3, 0), B(3,0, –2) and C(1, 4, 2). (a) Find the equation of the plane…

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Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any nonzero numbers a, b, and c. Which planes…

A: Given equation of plan is xa+yb+zc=1   ...(1) Where a, b, c≠0

Q: A plane meets the coordinate axes in A, B, C. If the centroid of aAl Show that the equation of the…

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Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (a, 0), (0,…

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Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…