Q4. (a) Express the given equation into cylindrical and spherical coordinates: (x + y)2 – z2 + 4 = 0 (b) find the equation of sphere through the circle x? + y² + z? = 1, 2x + 4y + 5z = 6 and touching the xz-plane.

Q: Convert z = 9x2 - 9y2 to cylindrical coordinates.

A: The objective of the question is to convert the given equation in Cartesian coordinates (x, y, z) to…

Q: 2. Convert the point (V6, , v2 ) from cylindrical to spherical coordinates. (12등, ) (b) (vZ;. )…

A:

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Convert parametric equations to a Cartesian X = tvo cose y = tvosine - gt² 2 X = y = - cost 2 sint +…

A:

Q: Consider the following vectors: -3 W₁ = -3 ,W2 = 10 V= 0 -3 -12 -2 The set B = {W₁, W₂} is an…

A: We have to find a vector n that is orthogonal to W, and such that v-n is in W.

Q: convert the point (3, -4, 5) in rectangular coordinates into both spherical and cylindrical…

A:

Q: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

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

A:

Q: Find the cylindrical equation for the surface whose rectangular equation is x² + y² - 2y = 0.

A: Given rectangular equation is,We have to find cylindrical equation for the surface.

Q: 2. Convert the point (V6, , V2 ) from cylindrical to spherical coordinates. (a) (V2,플, ) (b) (vz. )…

A: Option C is correct answer.

Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

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

A: The solution is given as