Straightforward vector calc problem

[tjaeger]

Studying for finals and I don't recall how to do projection and I don't like the explanation my textbook gives

Problem: Find the distance from the point (1,3,-2) to the plane 2x + y - z = 1

The answer to this problem should be sqrt(6)

Relevant equations: ?

The attempt at a solution:

I know I have to do a projection of using two vectors, and I know one of the vectors is the normal vector to the plane (2i + j + k). I'm not sure how to find the other vector using the point given and which of the vectors is projected onto the other.

 

[Hootenanny]

Welcome to the Forums,

Well, what equation / method are you using to find the distance from the point to the plane?

 

[mjsd]

draw a picture first...
consider an arbitrary point P on the plane, let Q=(1,3,-2)
now the magnitude of the proj of PQ in the direction of your normal vector IS the distance from Q to plane...

 

[tjaeger]

ok, thanks. I got it now.