Distance between the parallel lines $\frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1}$ and $\frac{x+4}{3}=\frac{y-3}{-2}=\frac{z+2}{1}$ is

The equation of the plane, passing through the mid point of the line segment of join of the points $\mathrm{P}(1,2,5)$ and $\mathrm{Q}(3,4,3)$ and perpendicular to it, is

The area of the triangle, whose vertices are $A \equiv(1,-1,2), B \equiv(2,1,-1)$ and $C \equiv(3,-1,2)$, is

The equation of the line, through $\mathrm{A}(1,2,3)$ and perpendicular to the vector $2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\hat{i}+3 \hat{j}+2 \hat{k}$, is