Question

Drive the equation of a plane perpendicular to a given vector and passing through a given point both in vector and Cartesian form.

Answer 1

(Vector form)

Equation of a plane passing through point A whose position vector is $\overrightarrow{a}$ and perpendicular to $\overrightarrow{n}$ is given by

$(\overrightarrow{r}-\overrightarrow{a})\cdot \overrightarrow{n}=0$

(Cartesian form)

Equation of a plane passing through point $(x_1,y_1,z_1)$ and perpendicular to a line with direction ratios $A,B,C$ is given by

$A(x-x_1)+B(y-y_1)+C(z-z_1)=0$