6. Convert from cylindrical to rectangular coordinates (a) (4, π/6, 3) (b) (8, 3π/4, -2) (c) (5, 0, 4) (d) (7, t, -9) 7. Convert from rectangular to spherical coordinates (a) (1,√3,-2) (b) (1,-1, √√2) (c) (0, 3√3, 3) (d) (-5√3, 5, 0) 8. Convert from spherical to rectangular coordinates (a) (5, π/6, π/4) (b) (7, 0, π/2) (c) (1, л, 0) (d) (2, 3π/2, π/2) 9. Convert from cylindrical to spherical coordinates (a) (√3, π/6, 3) (b) (1, π/4, -1) (c) (2, 3π/4, 0) (d) (6, 1, -2√3) 10. Convert from spherical to cylindrical coordinates (a) (5, π/4, 2π/3) (b) (1,7π/6, л) (c) (3, 0, 0) (d) (4 7/6 π/2)

Q: Change from rectangular to spherical coordinates. (a) (9, 3√3, 6) (P₁0, 9) = (12 (p, 0, ) = (5√2 T 6…

A: Given coordinates:- a) 9,33,6 b) 0,-5,-5

Q: [10] (3) Consider the triangle, A ABC, in R³, given that the three vertices are = B с = GIVEN: S is…

A:

Q: IQ5] Solve the following of A- Change from cartesian (i) (ii) (1,√3,-2√3) to Cylindrical and…

A: Cartesian coordinates (1,√3, -2√3)x= 1y= √3z=-2√3

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates.

A:

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0sos 2n, and 0 sos n.) (a) (0, 7, -7)…

A:

Q: Change from rectangular to spherical coordinates. (a) (9, 3/3, 6) (P, 0, p) = ( 12 ) (b) (0, 5, –5)…

A: Rectangle coordinates are (a)(9,33,6)(b)(0,5,-5)

Q: Find the equations r = g (0, z) (cylindrical) and p = f (0, 4) (spherical) for the hyperboloid x² =2…

A: To find-  Find the equation r = gθ, z (cylindrical) and ρ = fθ, ϕ (spherical) for the hyperboloid…

Q: (a) Convert the points from cylindrical coordinates to rectangular coordinates (2,–7,4) (b) Convert…

A: (a)  We know that cylindrical coordinates are ρ,θ,z Given cylindrical coordinates are 2,-π,4 So,…

Q: 1. Convert | 1,-/3, 3 from rectangular coordinates to cylindrical coordinates

A:

Q: Write the equation in spherical coordinates. (a) 5z2 = 8x2 + 8y2 (b) x2 + 3z2 = 7

A:

Q: lindrical coordinates. (Choose r> 0 and -2π ≤ 0 < 0).

A:

Q: 6. The point V (3,-5) is rotated 270° clockwise around the origin. Find the coordinates of the…

A: The given point is V(3, -5).

Q: Write the equation in spherical coordinates. (a) 5z2 = 8x2 + 8y2 (b) x2 + 3z2 = 7

A: Any point in the rectangular coordinate system is represented as x, y, z. Any point in the spherical…

Q: mange the point (-2,2, from rectangular to cylindrical coordinates and spherical coordinates. √²-25²…

A: Given ;  Point = (-2,2,1).

Q: Write the equations in cylindrical coordinates. (a) 7x2 - 8x + 7y2 + z2 = 7 (b) z = 2x2 - 2y²

A: The cylindrical coordinate is r, θ, z.

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as