Question

The foot of the perpendicular drawn from the origin to a plane is M(1, 2, 0). Find the vector equation of the plane.

Answer 1

The vector equation of the plane passing through A(\(\bar{a}\)) and perpendicular to \(\bar{n}\) is \(\bar{r}.\bar{n} = \bar{a}.\bar{n}\)

M(1, 2, 0) is the foot of the perpendicular drawn from origin to the plane. Then the plane is passing through M and is perpendicular to OM.

If \(\bar{m}\) is the position vector of M, then \(\bar{m}\) = \(\hat{i}.\)

Normal to the plane is

∴ the vector equation of the required plane is