- #1

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## Homework Statement

Given a plane S: x+y+z=8 and two points A(6,5,3) and B(10,5,-1), find the point P on plane S such that a line from point A bounces off of the plane S at point P and passes through point B.

## Homework Equations

## The Attempt at a Solution

If I know that the angle of incidence = the angle of reflectance, then I can also say that a normal vector from plane S bisects will these two points at point P. So if I can proove that the angle between vectors

**AP**and

**n**is the same as the angle between vectors

**BP**and

**n**then this should solve my problem. Well, this is what I tried to show at least, and did not come up with the angle between the two vectors to be the same.

I found my normal vector

**n**to be <1,1,1> and I took my point P to be (8,0,0). So, from there, I found vectors

**AP**and

**BP**to be <2,-5,-3> and <-2,-5,1> respectively.

Any help on which direction to go towards next would be a great help! Thank you!