Math Help - Point of intersection of a line with plane

1. Point of intersection of a line with plane

Find the coordinates of the point where the line $x = 2 - 3t$, $y = 1 + t$, $z = 4 - t$intersects the plane $2x - 3y + z = -16$

Please explain the solution with the logic behind it.

2. Just substiture the parametric values of x y and z into the deifnition of the plane so:-

becomes
2(2-3t) - 3(1+t) + (4-t) = -16

multiply out and gather terms yields
10t=21
t=2.1
So the line intersects theplane at the parametric value t = 2.1 which defines all the values of x, y and z
(x,y,z) = (-4.3,3.1,1.9)