Find the spherical coordinates for point p and find an

Question

Question:

A point P has rectangular coordinates (1, 0, 2 ) and lies on the surface of a sphere centred on the origin.

i) Find the spherical coordinates for point P.

ii) Find an equation for the surface of the sphere.

iii) Using spherical coordinates write a Matlab program that plots the surface of the sphere.

Submit your code and graph.

i) (x, y, z) = (1, 0, √2)

P = √(x² + y² + z²) = √(1² + 0² )+ √2² = √3

Q = tan^-1(y/x) = tan^-1(0/1) = 0

z = pcos(Φ)  

cos(Φ) = √2/√3

sin(Φ) = 1/√2

ii) x² + y² + z² = P²