If the plane $\frac{x}{2}-\frac{y}{3}-\frac{\mathrm{z}}{5}=1$ cuts the co-ordinate axes in points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ respectively, then the area of the triangle $A B C$ is

If the lines $x=a y-1=z-2$ and $x=3 y-2=\mathrm{bz}-2(\mathrm{ab} \neq 0)$ are coplanar, then

The Cartesian equation of the plane $\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ is

If the line $\frac{x-3}{2}=\frac{y+5}{-1}=\frac{z+2}{2}$ lies in the plane $\alpha x+3 y-z+\beta=0$, then values of $\alpha$ and $\beta$ respectively are ….