ABCD is a quadrilateral with $\overline{\mathrm{AB}}=\overline{\mathrm{a}}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}$ and $\overline{\mathrm{AC}}=2 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$. If its area is $\alpha$ times the area of the parallelogram with $\mathrm{AB}, \mathrm{AD}$ as adjacent sides, then the value of $\alpha$ is

The equation of a line passing through the point $(-1,2,3)$ and perpendicular to the lines $\frac{x}{2}=\frac{y-1}{-3}=\frac{z+2}{-2}$ and $\frac{x+3}{-1}=\frac{y+3}{2}=\frac{z-1}{3}$ is

If $A=\left[\begin{array}{rrr}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]$ then $A(I+\operatorname{adj} A)=$

A line L is passing through points $\mathrm{A}(1,3,2)$ and $\mathrm{B}(2,2,1)$. If mirror image of point $\mathrm{P}(1,1,-1)$ in the line L is $(x, y, z)$ then $x+y+\mathrm{z}=$