Coordinates of the points O, P, Q and R respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6) L, M, N and K OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length $$\sqrt 2 $$ ?

The line $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ is given by

Consider the following statements

1. The angle between the planes 2x $$-$$ y + z = 1 and x + y + 2z = 3 is $${\pi \over 3}$$

2. The distance between the planes 6x $$-$$ 3y + 6z + 2 = 0 and 2x $$-$$ y + 2z + 4 = 0 is $${{10} \over 9}$$

Which of the above statement is/are correct?

Let the coordinates of the points A, B, C be (1, 8, 4), (0, $$-$$11, 4) and (2, $$-$$3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC ?