A plane containing the point (3,2,0) and the line x-11=y-25=z-34 also contains the point:

Question

A plane containing the point $(3,2,0)$ and the line $\dfrac{x-1}1=\dfrac{y-2}5=\dfrac{z-3}4$ also contains the point:

Accepted Answer

Plane $A(x-1)+B(y-2)+C(z-3)=0$ with $A+5B+4C=0$ and, through $(3,2,0)$, $2A-3C=0$.
$$\frac{A}{-15}=\frac{B}{9}=\frac{C}{-10}\implies A=-15k,B=9k,C=-10k.$$
Plane: $-15(x-1)+9(y-2)-10(z-3)=0$. Testing $(0,-3,1)$: $15-45+20=0$ .

Solutions · 1