Does the sphere x + y + ? = 25 have symmetry with %3D respect to a) the xy-plane? b) the line e: (x, y, z) = (-1, 2, 3) + n(1, –2, – 3)?

Q: Consider the points A=(2,7,-4) and B=(4,5,7) in R3, one way to write the parametric equation of the…

A: Given :- Consider the points A = (2, 7, - 4) and B = (4, 5, 7) in R³, To find:- one way to write the…

Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

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

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Q: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

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Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: A sphere, Si is given by the equation: r? + y² + 22 – 2x – 4y + 8z + 17 = 0 (a) Write the equation…

A: (a) Consider the given information. x2+y2+z2-2x-4y+8z+17=0 Now, write the equation in the standard…

Q: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .

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Q: 2) Consider two spheres (x - 2)² + (y - 3)² + z² = 1 x² + y² + z² = -8y + 2z + 3 a. What is the…

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…