The position vectors of the points $A$ and $B$ are respectively $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If the points $P$ and $Q$ are respectively the orthogonal projections of $A$ and $B$ on the plane $x+y+z=3$, then $P Q=$

If $A(4,3,2), B(5,4,6), C(-1,-1,5)$ are the vertices of a triangle, then the coordinates of the point in which the bisector of the angle $A$ meet the side $B C$ is

Assertion (A) The direction ratios of line $L_1$ are 2, 5, 7 and those of line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. The lines $L_1, L_2$ are parallel.

$\boldsymbol{\operatorname { R e a s o n }}(R)$ The direction ratios of a line $L_1$ are $a_1, b_1, c_1$ and those of another line $L_2$ are $a_2, b_2, c_2$. The lines $L_1$ and $L_2$ are parallel if $a_1 a_2+b_1 b_2+c_1 c_2=0$

The correct option among the following is

If $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}$ lies in the plane $a x+b y+z=7$, then $a+b=$