Find the point in which the line through the origin perpendi

Solution

Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through the point (0,0,0). r(t) = r0 + vt r(t) = <2t, -t, -t> Meaning: x = 2t y = -t z = -t This has to coincide with the plane, so we can simply sub in these points in the other equation to solve for t. 3(2t) - 5(-t) + 2(-t) = 6 6t + 5t - 2t = 6 9t = 6 t = 2/3 Plug the values of t back in for the line equation r(2/3) = <4/3, -2/3, -2/3> Point: (4/3, -2/3, -2/3)