Write the plane ` vec rdot((2 hat i+3 hat j-6 hat k)=14` in normal form.

Explanation

`\vec{r} \cdot \vec{n}=d \quad \vec{n}=2 \hat{\i}+3 \hat{\i}-6 \hat{k}`


`|n|=\sqrt{4+9+36}=\sqrt{49}=\pm 7`

Normal form
`\pm \vec{r} \cdot\(\frac{2}{7} \hat{\i}+\frac{3}{7} \hat{\j}-\frac{6}{7} \hat{k}) \equiv 2.`