The equation of a plane containing the line x+1-3=y-32=z+21 and the point (0,7,-7) is

Question

The equation of a plane containing the line $\dfrac{x+1}{-3}=\dfrac{y-3}2=\dfrac{z+2}1$ and the point $(0,7,-7)$ is

Accepted Answer

Plane $a(x+1)+b(y-3)+c(z+2)=0$ with $-3a+2b+c=0$ (contains the line) and, through $(0,7,-7)$: $a+4b-5c=0$.
Solving gives $a=b=c=1$ (up to scale). Plane: $(x+1)+(y-3)+(z+2)=0\implies x+y+z=0$.

Solutions · 1