Hard geometry question need help (vectors planes spheres)
In a space with an orthonormal coordinate system consider
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.