Comment
Share
Q)

# Let $P(3,2,6)$ be a point in the space and Q be a point on the line $\overrightarrow{r} =(\hat i - \hat j +2 \hat k) +\mu (-3 \hat i +\hat j +5 \hat k ),$ then find the value of $\mu$ for ehich the vector $\overrightarrow{PQ}$ is parallel to the plane $x -4y+3z=1$

Condition for parallelism is $\sin \theta = \overrightarrow{b} . \overrightarrow{n}=0$
The line joining the point $P(3,2,6)$ and Q which lies on the line is
$PQ= (-3k-3) +(\mu -3) j +5 (\mu -6) k$
$\therefore [(-3\mu -3) \hat i +(\mu -3) \hat j +( 5 \mu -6) \hat k ], (\hat i - 4 \hat j +3 \hat k]= -3 \mu -3 -4 \mu +12+15 \mu -18=0$
$8 \mu -9=0$
$\mu =\large\frac{9}{8}$