The angle between the lines $x-3 y-4=0,4 y-z+5=0$ and $x+3 y-11=0,2 y-z+6=0$ is

If the area of parallelogram, whose diagonals are $\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$ and $2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\alpha \hat{\mathrm{k}}$ is $\frac{\sqrt{93}}{2}$ sq. units, then $\alpha=$

The correct constraints for the given feasible region are ….

The circumradius of the triangle formed by the lines $x y+2 x+2 y+4=0$ and $x+y+2=0$ is