Answer:
The equation of plane is:
r→=(2i^–j^+3k^)+λ(3i^–j^+2k^)\vec{r}=(2 \hat{i}-\hat{j}+3 \hat{k})+\lambda(3 \hat{i}-\hat{j}+2 \hat{k})
On comparing with 
Here, 
The equation of plane
r→·(i+j+k^)=3\vec{r} \cdot(i+j+\hat{k})=3
On comparing with 
\vec{n}=(i+j+\hat{k})
Let ‘ 
![\[\begin{aligned} \sin \theta &=\left|\frac{\vec{b} \cdot \vec{n}}{|\vec{b}||\vec{n}|}\right| \\ \therefore \sin \theta &=\left|\frac{(3 i-j+2 k) \cdot(\hat{i}+\vec{j}+\vec{k})}{\sqrt{9+1+4} \sqrt{1+1+1}}\right| \\ \therefore \sin \theta &=\frac{3-1+2}{\sqrt{14} \cdot \sqrt{3}}=\frac{4}{\sqrt{14} \sqrt{3}}=\frac{4}{\sqrt{42}} \\ \therefore \theta &=\sin ^{-1}\left(\frac{4}{\sqrt{42}}\right) \end{aligned}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8535c6b6f8a9a5363232edf87bfb1a08_l3.png "Rendered by QuickLaTeX.com")
