# Hard geometry question need help (vectors planes spheres)

the points

P(0, - 1, 1) and Q(3, 0, - 3) .

the line

d:

x = 2t

y = t , t included in R

z = 2 + 2t

the sphere

S: x ^ 2 + y ^ 2 + z ^ 2 - 2x - 2y + 2z - 6 = 0

and the plane

sigma : 2 * x - y + 4 = 0

a) The plane pi contains the point P and the line d Show that x + 2y - 2z + 4 + 0 is an equation of pi

b) Find the coordinates of the centre C and the radius R of the sphere S.

c) Find an equation for each of the two spheres with radius r = 3 which are tangential to at the point P. Verify that one of these spheres is S.

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This is a time consuming problem. I suggest you to offer a bounty.