Thread: Vector equation of a line problem

I need to find a line that passes through the point P (4,3,2) and is perpendicular to the line (1+2t, -1+t, 1-3t).

I only managed to use the dot product to get 2x +y-3Z =0 I have no idea how to proceed to get the exact values of x,y,z that passes through 4,3,2.

Any help will be appreciated.

Hi

The point P (4,3,2) and the line (1+2t, -1+t, 1-3t) determine a plane.
You can draw a sketch of this plane if you like.
Let be the orthogonal projection of P on the line.

H being on the line there exists such that




(PH) being perpendicular to the line the dot product of PH and (2,1,-3) is equal to 0


Substituting with and so on ... you can fnd the value of then the coordinates of H, then the coordinates of PH, from which you can find an equation of (PH)