A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals?

D. Direction cosines of the line are 1/√3, 1/√3, 1/√3.
Any point on the line at a distance t from P(2, -1, 2) is (2 + t/√3, -1 + t/√3, 2 + t/√3), which lies on 2x + y + z = 9.
⇒ 2(2 + t/√3) + (-1 + t/√3) + (2 + t/√3) = 9
⇒ 4 + 2t/√3 - 1 + t/√3 + 2 + t/√3 = 9
⇒ 5 + 4t/√3 = 9
⇒ 4t/√3 = 4
⇒ t = √3