Particle pierces a sphere (vector)

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A particle starts from point (-2,1,2) with velocity vector v = < 1,1,0 > and hits the plane x + z = 2 and bounces off and penetrates through a sphere x² + y² + z² = 25 at two points, P and Q. What is the angle between OP and OQ.

This was a question on one of my exams that I did not get. I cannot remember completely, but I think the OP and OQ are vectors sharing the origin of the coordinate system as their vertex and we want to find that angle between them.

So I am trying to work this one out and I am getting really stuck.

I started by parametrizing the starting point and vector and came up with:

x = -2 + t
y = 1 + t
z = 2

where t = 2

I also know that the angle of incidence will = the angle of reflectance, so v = -u = < -1,1,0 > (is this statement true?)

But I don't see how I can relate this to the angle between P and Q
 

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