If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, then the length of $P M$ is

If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{C D}$ is

Consider the following statements:

Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}$, $\frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then, the lines $L_1, L_2$ are parallel.

Reason : ( $\mathbf{R}$ ) If the direction ratios of a line $L_1$ are $a_1, b_1, c_1$ the direction ratios of a line $L_2$ are $a_2, b_2, c_2$ and $a_1 a_2+b_1 b_2+c_1 c_2=0$, then the lines of $L_1, L_2$ are parallel.

A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of $X$-axis, then $\cos \alpha=$