Find the angle between the line and the plane
Find the angle between the line and the plane

The equation of plane is:

$\stackrel{\to }{r}=\left(2\stackrel{^}{i}–\stackrel{^}{j}+3\stackrel{^}{k}\right)+\lambda \left(3\stackrel{^}{i}–\stackrel{^}{j}+2\stackrel{^}{k}\right)$

\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

$\stackrel{\to }{r}·\left(i+j+\stackrel{^}{k}\right)=3$

\vec{r} \cdot(i+j+\hat{k})=3

On comparing with

$\stackrel{\to }{n}=\left(i+j+\stackrel{^}{k}\right)$

\vec{n}=(i+j+\hat{k})

Let ‘ ‘ be the anyle between line and plane