The point in the $X Y$ - plane which is equidistant from the points $A(2,0,3), B(0,3,2)$ and $C(0,0,1)$ has the coordinates

If the direction ratio of two lines $L_1$ and $L_2$ are given by $(1,-2,2)$ and $(-2,3,-6)$ respectively, then the direction ratios of the line which is perpendicular to the linesh and $L_2$ are

If the image of the point $A(1,1,1)$ with respect to the plane $4 x+2 y+4 z+1=0$ is $B(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

Assertion (A) For the lines $\mathbf{r}=\mathbf{a}+t \mathbf{b}$ and $\mathbf{r}=\mathbf{p}+s \mathbf{q}$, if $(\mathbf{a}-\mathbf{p}) \cdot(\mathbf{b} \times \mathbf{q}) \neq 0$, then the two lines are coplanar.

Reason $(\mathrm{R})|(\mathbf{a}-\mathbf{p}) \cdot(\mathbf{b} \times \mathbf{q})|$ is $|\mathbf{b} \times \mathbf{q}|$ times the shortest distance between the lines $\mathbf{r}=\mathbf{a}+t \mathbf{b}$ and $\mathbf{r}=\mathbf{p}+s \mathbf{q}$.