Question

Find the vector equation of a plane which is at 42 unit distance from the origin and which is normal to the vector 2i + j - 2k.

Answer 1

If \(\hat{n}\) is a unit vector along the normal and p is the length of the perpendicular from origin to the plane, then the vector equation of the plane is \(\bar{r}.\hat{n} = p\)

∴ the vector equation of the required plane is