Question

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

• A. $x+2y+2z=0$
• B. $-13x+3y-3z=42$
• C. $x+y+z=1$
• D. $x+y+z=0$

Answer 1

The correct option is D $x+y+z=0$

The equation of the plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ is
$a(x+1)+b(y-3)+c(z+2)=0\cdots \left(i\right)$
where $-3a+2b+c=0\cdots \left(ii\right)$
As plane also contains point $(0,7,-7),$ we have
$\Rightarrow a(0+1)+b(7-3)+c(-7+2)=0$
$\Rightarrow a+4b-5c=0\cdots \left(iii\right)$
Solving $\left(ii\right),\left(iii\right)$
$\frac{a}{-14}=\frac{b}{-14}=\frac{c}{-14}=k\text{(Let)}$
we get, $a=k,b=k$ and $c=k$
putting in equation $\left(i\right)$
$(x+1)+(y-3)+(z+2)=0$
$\Rightarrow x+y+z=0$