A point P lies on a line through Q(1, $$-$$2, 3) and is parallel to the line $${x \over 1} = {y \over 4} = {z \over 5}$$. If P lies on the plane 2x + 3y $$-$$ 4z + 22 = 0, then segment PQ equals

The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, $$-$$11, 4) and (2, $$-$$3, 1) is

The equation of the plane through (1, 2, $$-$$3) and (2, $$-$$2, 1) and parallel to X-axis is

Three lines are drawn from the origin O with direction cosines proportional to (1, $$-$$1, 1), (2, $$-$$3, 0) and (1, 0, 3). The three lines are