To measure the distance from a point, A, to a plane, p, you measure along the line through A perpendicular to the plane, p. That's true because a leg of a right triangle is always shorter than the hypotenuse. Further, if the vector is written as Ax+ By+ Cz= D as yours is, then the vector <A, B, C> is perpendicular to the plane. So you want to measure the distance from A to p, you want a line that passes through P and is in the direction of the vector <A, B, C>. Okay, a line through point in the direction of vector <A, B, C> is given by the parametric equations , , . Here, you are given the equation of the plane so you know A, B, and C. You are given the point so you know , , and . Use that information to write the equation of the line through (3, 0, -1) perpendicular to 4x+ 2y- z= 6. The point at which that line intersects the plane (replace x, y, and z in the equation of the plane by there expressions in terms of t for the line and solve for t) is the point on the plane closest to .