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 - X. y. z a b c %3D

Q: Which plane in the figure below intersects plane EHAC to form AH? G H. D C A O plane ABCD O plane…

A: Given query is to find indicated plane.

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: Look carefully at each figure below showing the intersection of a plane with a solid. For each…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 8x - 4y + z = 3 x + 3y + 4z = 1 O…

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Q: Let ABCD be a trapezoid with bases BC and AD. Let 0 = AB n DC be the point at which the lines…

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

A: Given that vertices= (0, 0), (a, 0), (a / 2, b)

Q: Evaluate | x? zdS, where S is the part of the plane z = 2 + 4x + y above the rectangle [0, 4] × [0,…

A: To evaluate: ∫∫Sx2z dS where S is the part of the plane z=2+4x+yabove the rectangle region…

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: z = 9x? + 9y? O b. z= 3x2 + 3y? O c. z= 4x? + 4y? O d. z= x2 + y? z = (x – 3)2 + y² Oc. O e.

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Q: a) Solve the equation ru, + tu, D0 with u(r, 0) = e. b) In which region of the zt plane is the…

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Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

A: a) The points are A(0,−40, 0) and B (40, 0,⎯20)A0,-40, 0 and B (40, 0,-20) Obtain the distance AB:…

Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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Q: Consider the plane makes intercepts of 2 A, 3A, 4A on the coordinate axis of the crystal with…

A: the Intercepts are 2A˙,3A˙,4A˙         (1)  a:b:c=4:3:2                  (2) take the ratio of (1)…

Q: In the triangle below, O is the centroid. Find the length of median XP. 3x 2x-7 Y XP

A: Given, OP = 2x - 7 OX = 3x  So, According to the figure XP = OX + OP      = 3x + 2x - 7       = 5x -…

Q: In the parallelepiped below, we know that (ū A ü). W = 6. Additionally, ū = (1, 1, 0) and i= (0, 1,…

A: Given that:                        (u∧v).w=6u=(1,1,0)v=(0,1,1)

Q: Look carefully at each figure below showing the intersection of a plane with a solid. For each…

A: Given query is to find the 2 dimensional shape of cross sections.

Q: Sections ABCD is a quadrilateral having the given coordinates A(2, 3), B(8, 9), C(11, 3), and D(11,…

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Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

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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: a. A trapezoid has been transformed on the coordinate plane as shown. Trapezoíd A Trapezoid B

A: Given that:

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: 2. Sketch a graph of the set of points which satisfy the following conditions. The coordinate…

A: In rectangular co-ordinate system:x= 2, is a yz-plane passing through x= 2.

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: Write an equation for the plane that contains the x-axis and the point (0, 8, 24). O 3 = x² + y? +…

A: Please refer the attached image for complete solution.

Q: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

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Q: Below is a square pyramid. For each plane described, what is the cross section that results form the…

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

A: given

Q: Given: G is the centroid of isosceles triangle AEC, where angle A and angle C are equal and AB = 6…

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Q: In computer graphics and perspective drawing, we need to represent objects seen by the eye in space…

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

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Q: // 2° zdS, where S is the part of the plane z = 4+ 2æ + y above the rectangle [0, 5] × [0, 3]…

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

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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: (a) Describe the 3 dimensional shape determined by the equation below. 12 - 2r – 26 + y² + 4y + 2² –…

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Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

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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: (a) Find the image AA'B'C' of AABC under the rigid motion consisting of three consecutive…

A: Answer is mentioned below

Q: Let u = 2 and v = | 0 , and let P = span{u, v}. Find an equation for the plane P.

A: Given: Let xyz be a point in Span {u, v} so there are t, r∈ℝ such that xyz=tu+rv. So,…

Q: The plane can perpendicular to the a) x-axis at (3, 0, 0) b) z-axis at (0, 0, -2) c) y-axis at (0,…

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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: EK does not appear to be parallel to the plane containing which points? d. Q. S, C а. U. A. С b. Q.…

A: Parallel lines are two or more lines that lie in the same plane and never intersect. To show that…

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: ind an equation for the plane that passes through the point A(1,2,3)parallel to u = 2i + 3 j + k nd…

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Q: Which one of the following equations describes the plane passing through the points (1, 1, 0), (0,…

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