If the position vectors of two points $P$ and $Q$ are respectively $9\hat{i} - \hat{j} + 5\hat{k}$ and $\hat{i} + 3\hat{j} + 5\hat{k}$,and the line segment $PQ$ intersects the $YOZ$ plane at a point $R$,then the ratio $PR : RQ$ is equal to

$A$ line having direction ratios $1, -4, 2$ intersects the lines $\frac{x-7}{3} = \frac{y-1}{-1} = \frac{z+2}{1}$ and $\frac{x}{2} = \frac{y-7}{3} = \frac{z}{1}$ at the points $A$ and $B$ respectively. Then,the coordinates of points $A$ and $B$ are:

The angle between the lines $3x + 2y + z = 0 = x + y - 2z$ and $2x - y - z = 0 = 7x + 10y - 8z$ is

If the line joining the points $A(2, 3, -1)$ and $B(3, 5, -3)$ is perpendicular to the line joining the points $C(1, 2, 3)$ and $D(3, y, 7)$,then $y=$

The square of the distance of the point $P(5,6,7)$ from the line $\frac{x-2}{2} = \frac{y-5}{3} = \frac{z-2}{4}$ is equal to:

Let $A(\alpha, 4, 7)$ and $B(3, \beta, 8)$ be two points in space. If the $YZ$ plane and $ZX$ plane respectively divide the line segment joining the points $A$ and $B$ in the ratio $2:3$ and $4:5$,then the point $C$ which divides $\overline{AB}$ in the ratio $\alpha: \beta$ externally is