The plane containing the line x-11=y-22=z-33 and parallel to the line x1= y1= z4 passes th…

Question

The plane containing the line $\dfrac{x-1}1=\dfrac{y-2}2=\dfrac{z-3}3$ and parallel to the line $\dfrac x1=\dfrac y1=\dfrac z4$ passes through the point:

Accepted Answer

Plane $a(x-1)+b(y-2)+c(z-3)=0$ with $a+2b+3c=0$ (contains the line) and $a+b+4c=0$ (parallel to $(1,1,4)$).
$$\frac a{8-3}=\frac b{3-4}=\frac c{1-2}\implies a=5k,\ b=-k,\ c=-k.$$
Plane: $5(x-1)-(y-2)-(z-3)=0\implies5x-y-z=0$. Testing $(1,0,5)$: $5-0-5=0$ .

Solutions · 1