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August 24, 2016
Posted by **J** on Saturday, May 26, 2012 at 10:07am.

- Calculus -
**MathMate**, Sunday, May 27, 2012 at 7:18amFind the shortest distance from a point P(2,-1,2) to a line L r= [-1,0,7] + t [4,1,-2].

Assume a point Q on the line such that PQ is the shortest possible distance between them.

Then PQ is orthogonal to the line L.

Given P(2,-1,2).

Let Q(-1+4t, 0+t, 8-2t), then

PQ=<-3+4t, t-1, 6-2t>

and we look for the value of t such that

PQ.<4,1,-2>=0

or

<-3+4t, t-1, 6-2t>.<4,1,-2>=0

⇒

4(-3+4t)+(t-1)-2(6-2t)=0

Can you solve for t?