The distance between a line L and a point P that is not on the line is defined to be the shortest distance between that point and any point on the line. Us dot product projection to:
take an arbitrary point A on L
Find the vector AP and set equal to a
resolve vector a=AP into components parallel and perpendicular to the line.
demonstrate that the distance from P to L is the magnitude of the perpendicular component. Compute this magnitude.
You can also use the parallel component to find the point on the line that is closest to point P. Here are the numbers:
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Line L goes through the point whose position vector is <1,-2,0> and is parallel to the vector u=<3,1,2>. The point P has position vector p=<-1,1,2>