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

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Q: 6. Find the intersection of the line / and the plane . 1:7=(4,-1,4) +t(5,-2,3) x: 2x+5y+z+2=0

A: Given is the equation of line as l:r→=(4,-1,4)+t(5,-2,3) Equation of plane as π: 2x+5y+z+2=0 First…

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: area of the square

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Q: a) [ ] Show that the equation 4x8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

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 shortest distance between the: x−1_y−3 a. point (1, 3, 2) and the line *-¹-y-3_2–7 1 -1 2…

A: Given planes:- P1: x+2y-5z-10=0 P2: 2x+4y-10z-17=0

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

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: 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: 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…