Let T be the plane x-y+3z=15. Find the shortest distance d from the point p0=(-2, 4, 4) to T, and the point Q in T that is closest to p0. Use the square root symbol where needed to give an exact value for you answer.

Answer 1

the distance is

|-2-4+3*4-15|/√(1+1+9) = 9/√11

I'll have to get out my math book to figure out Q, but you should have some examples in your text. Also google can surely provide similar solved exercises.