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 ofPHand (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 ofPH, from which you can find an equation of (PH)