Given are the line l:m*(6/2/3) and the point P(2/1/2). Sought is the point Q on l with the shortest distance to P.
I know the solution of inventing a plane E with normal vector N which equals (6/2/3), but I'd liek to know why the following approach doesn't work as well:
The vector QP must be normal to the direction vector of the line, so (6/2/3)*QP = 0. Point Q is given with (m6/m2/m3), thus the vector QP is (2-6m)/(1-2m)/(2-3m).
m=no m valid for all three
Why doesn't that lead to a correct solution?
Can anyone help?