Consider the two lines

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$ and $${L_2}:{{x - 2} \over 1} = {{y + 2} \over 2} = {{z - 3} \over 3}$$

The unit vector perpendicular to both the lines L₁ and L₂ is

The distance between the line $$r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda (\widehat i - \widehat j + 4\widehat k)$$ and the plane $$a\,.\,(\widehat i + 5\widehat j + \widehat k) = 5$$ is

A line passing through P(3, 7, 1) and R(2, 5, 7) meet the plane 3x + 2y + 11z $$-$$ 9 = 0 at Q. Then PQ is equal to