Z A Consider the tetrahedron ABCD with vertex A at the origin as shown: (a) Find the equation of the line through vertices B and D: D(6,0,0) X Determine the face angle where edges BD and BC meet, to the nearest degree. Find the scalar equation of the plane containing vertices B, C and D: (b) B(0,0,3) ---->y ->y C(0,4,0)

Q: In the first step, when you assumed the equation of the plane is az+by+cz=1 where did the 1 come…

A: Let the equation of the plane is .

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

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Q: Consider the tetrahedron formed by the four points P(0, 0, 0), Q(8, 0, 0), R(0,6, 0), and S(0, 0,…

A: Given: A tetrahedron that passes through P(0,0,0), Q(8,0,0), R(0,6,0), and S(0,0,4). (a) To Find:…

Q: Consider the equation z = x² + y. (a) Describe the traces of the equation parallel to the xz-plane,…

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Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: a) y = (x - 4)² b) у 3 (х — 2)2 -4 c) y = (x + 3)² – 2

A: (a) In the given equation y=(x-4)2, At x=0 and x=8, y=16 At y=0, x=4. Thus, the x-intercept of the…

Q: Q3: a) Find an equation for the plane through P(0,1,-2) perpendicular to n= 3i- 2j+k

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Q: Write the equation of the parabola with vertex at (-9, 0) and directrix at x = -10 a) + 9 1,2 49 b)…

A: Given

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: The following equation represents a sphere: x² + y² + z² = 1. Which one of the following is the…

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Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

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Q: z = 8x² + 8y² + 18 nearest the plane 8y - 3x - 7z = 0.

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Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

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Q: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Q2-) The parallelogram shown in figur A(2, -1, 4), B(1, 0, -1), C(1,2,3) and D. Find: a- The…

A: Note:- This is multiple sub parts question and according to our company guideline i am doing first 3…

Q: b) Find the equation of the plane given by the shaded graph below C(0,0.3) B(0,2.0) y A(1,0,0)

A: Topic- equation of plane in 3D

Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: Find an equation for the plane through А (0, 0, 1), B (2, 0, 0), and С (), 3, 0).

A: The equation of a plane passing through three points Ax1, y1, z1, Bx2, y2, z2 and Cx3, y3, z3 is…