Question

Equation of the plane passing through the intersection of the planes $x+y+z=6$ and $2x+3y+4z+5=0$ and the point $(1,1,1)$ is

• A. $20x+23y+26z-69=0$
• B. $31x+45y+49z+52=0$
• C. $8x+5y+2z-69=0$
• D. $4x+5y+6z-7=0$

Answer 1

The correct option is A $20x+23y+26z-69=0$

Equation of required plane is
$(x+y+z-6)+\lambda (2x+3y+4z+5)=0....\left(i\right)$
which is passing through $(1,1,1)$.
$\therefore (1+1+1-6)+\lambda (2+3+4+5)=0$
$\Rightarrow -3+\lambda \left(14\right)=0$
$\Rightarrow \lambda =\frac{3}{14}$
On putting $\lambda =\frac{3}{14}$ in Eq. (i), we get
$(x+y+z-6)+\frac{3}{14}(2x+3y+4z+5)=0$
$\Rightarrow 20x+23y+26z=69$.