Question

Find the equation of the plane passing through the point $\left(-1,-2,1\right)$ having $\left(1,3,-2\right)$ as the direction ratios of the normal to the plane.

Answer 1

The equation of the plane passing through point $(-1,-2,1)$ having $(1,3,-2),$

$(a,b,c)=(1,3,-2)$

$(x,y,z)=(-1,2,1)$

Equation of plane:

$a(x-x_1)+b(y-y_1)+c(z-z_1)=0$

$\Rightarrow 1(x+1)+3(y+2)+(-2)(z-1)$

$\Rightarrow x+1+3y+6-2z+2=0$

$\Rightarrow x+3y-2z+9=0$