Question

Find the shortest distance from the point P= (-6, 1, 2 ) to a point on the line given by l: (x,y,z)= (3 t, -7 t, 6 t).
The distance is ?

Answer 1

shortest distance to a line

Answer 2

from a point

Answer 3

that is what we are looking for. So since the line goes through the origin, we should be able to use projections. I just can't get the right answer.

Answer 4

this explains it very well

Answer 5

https://www.youtube.com/watch?v=0lG53-ogF2k

Answer 6

find the projection and subtract it from OP