Find the coordinates of the point where the line through the point (3, ?, ?) and (2, ?, 1) crosses the plane 2x+y+z=7.

The parametric representation of the line can be written as r=(3, ?, ?)+t[(3-2), (? - ?), (? - 1)]=(3, ?, ?)+t(1, ?, ?) Thus, a point on the line would have coordinates as under: x=3+t, y=? -t, z=? +t Since this point has to also lie on the plane, we substitute the coordinates into the plane equation and obtain 2(3+t)+(? -t)+(? +t)=7 ⇒6+2t ? -t ? +t=7 ⇒ ? +t=7 ⇒ 5t=12 or t=Re-substituting t in the coordinates, we get x=3+=1, y=? -t=, z=? +12=7 The point is thus (1, , 7)