Question

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

• A. $x+y+z=1$
• B. $x+y+z=2$
• C. $x+y+z=0$
• D. None of the above

Answer 1

Answer: (C)

$x+y+z=0$

The equation of the plane containing the line
$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ is
$a(x+1)+b(y-3)+c(z+2)=0.....\left(i\right)$
where, $-3a+2b+c=0.....\left(ii\right)$
This passes through $(0,7,-7)$
$\therefore a+4b-5c=0....\left(iii\right)$
From Eqs. (ii) and (iii), we get
$\frac{a}{-14}=\frac{b}{-14}=\frac{c}{-14}$ or $\frac{a}{1}=\frac{b}{1}=\frac{c}{1}$
So, the required plane is $x+y+z=0$.