The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are

If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respectively, then equation of the plane containing $L_1$ and $L_2$ is

Let $O(\mathbf{O}), A(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}), B(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{k}}), C(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})$ and $D(4 \hat{\mathbf{k}})$ are position vectors of the points $O, A, B, C$ and $D$. If a line passing through $A$ and $B$ intersects the plane passing through $O, C$ and $D$ at the point $R$, then position vector of $R$ is

The distance of the point $O(\mathbf{O})$ from the plane $\mathbf{r}$. $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=5$ measured parallel to $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ is