If $d$ is the distance of point (2, 5, 10) from the plane containing the lines $\bar{r} = (4\hat{j} - \hat{k}) + \lambda(\hat{i} + 2\hat{j} - 2\hat{k})$ and $\bar{r} = (2\hat{i} + \hat{j}) + \mu(\hat{i} + 2\hat{j} - 2\hat{k})$, then $d^2 = $

The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are

The lines $\dfrac{x - 2}{1} = \dfrac{y - 3}{1} = \dfrac{z - 4}{-k}$ and $\dfrac{x - 1}{k} = \dfrac{y - 4}{2} = \dfrac{z - 5}{1}$ are coplanar if

The direction ratios of the normal to the plane passing through (1, 0, 0), (0, 1, 0) which makes an angle of measure $45^\circ$ with the plane $2x + 3y = 7$ are....