Find the equation of lane passing through the point ` hat i+ hat j+ hat k` and parallel to the point ` -> rdot(2 hat i- hat j+2 hat k)=5.`

Explanation

`vec{r} cdot hat{n}=vec{a} cdot vec{n}`


`vec{a}=hat{i}+hat{j}+hat{k}`


`vec{n}=2 hat{i}-hat{j}+2 hat{k}`


`vec{r}(2 hat{j}-hat{j}+2 hat{k})=(hat{i}+hat{j}+hat{k})(2 hat{i}-hat{j}+2 hat{k})`


`=(1)(2)+(1)(-1) +(1)(2)`


`=2-1+2`


`=3`


`vec{r}(2 hat{i}-hat{j}+2 hat{k})=3 rightarrow` equation.