Question

What is the equation of a plane?

Answer 1

The equation of a plane passing through the point $\left(x_1,y_1,z_1\right)$ with direction ratios $A,B,C$ is,

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

At least one of the values of $A,B,C$ must be non-zero.

• The equation of plane parallel to $xy$ is $z=c$.
• The equation of plane parallel to $yz$ is $x=a$.
• The equation of plane parallel to $xz$ is $y=b$.
• The equation of plane passes through the origin is $Ax+By+Cz=0$, where $A,B,C$ ar direction ratios of the plane.