If $L$ is a line common to the planes $3 x+4 y+7 z=1$, $x-y+z=5$, then the direction ratios of the line $L$ are

If the points $(1,1, \lambda)$ and $(-3,0,1)$ are equidistant from the plane $3 x+4 y-12 z+13=0$, then the values of $\lambda$ are

The shortest distance between the lines

$$ \begin{aligned} & \mathbf{r}=(3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})+t(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \text { and } \\ & \mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-4 \hat{\mathbf{k}})+s(6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \text { is } \end{aligned} $$

If $A(0,3,4), B(1,5,6), C(-2,0,-2)$ are the vertices of a $\triangle A B C$ and the bisector of angle $A$ meets the side $B C$ at $D$, then $A D=$