Find the value of m for which the line is parallel to the plane
Find the value of m for which the line is parallel to the plane

Given equation of line,

Comparing with the line ,

Comparing with

Since the line is paralle! to the plane

$\begin{array}{l}⇒\stackrel{\to }{b}·\stackrel{\to }{n}=0\\ ⇒\left(2\stackrel{^}{i}–m\stackrel{^}{j}–3\stackrel{^}{k}\right)·\left(m\stackrel{^}{i}+3\stackrel{^}{j}+\stackrel{^}{k}\right)=0\\ ⇒2m–3m–3=0\\ ⇒–m–3=0\\ ⇒m=–3\end{array}$

\begin{array}{l}

\Rightarrow \vec{b} \cdot \vec{n}=0 \\

\Rightarrow(2 \hat{i}-m \hat{j}-3 \hat{k}) \cdot(m \hat{i}+3 \hat{j}+\hat{k})=0 \\

\Rightarrow 2 m-3 m-3=0 \\

\Rightarrow-m-3=0 \\

\Rightarrow m=-3

\end{array}