Question

What is the equation of the plane through the point $(1,4,-2)$ and parallel to the plane $-2x+y-3z=7$?

Answer 1

Equation of the plane passing through the point $(1,4,-2)$ is

$A(x-1)+B(y-4)+C(z+2)=0$ ----- $\left(1\right)$

Since the plane is parallel to the plane

$-2x+y-3z=7$

So,

$\frac{A}{-2}=\frac{B}{1}=\frac{C}{-3}=k$ (K is any constant)

$A=-2k,B=k,c=-3k$

Putting the values of $A,B,C$ in equation $\left(1\right)$

$\begin{array}{c}-2k(x-1)+k(y-4)-3k(z+2)=0\\ \\ -2(x-1)+y-4-3(z+2)=0\\ \\ -2x+2+y-4-3z-6=0\\ \\ 2x-y+3z+8=0\end{array}$

This is the required equation of the plane .