Question

Equation of a plane through the line of intersection of planes $2x+3y-4z=1$ and $3x-y+z+2=0$ and it makes an intercept of $4$ on the positive $x$-axis is $2x+3y-4z-1+\lambda (3x-y+z+2)=0$, then $\lambda$ is

• A. $\frac{1}{2}$
• B. $30$
• C. $7$
• D. $-\frac{1}{2}$

Answer 1

Answer: (D)

$-\frac{1}{2}$

Equation of plane passing through intersection of plane $2x+3y-4z-1=0$ and $3x-y+z+2=0$ is given by,
$2x+3y-4z-1+\lambda (3x-y+z+2)=0$
Now intercept of this plane is $4$ on the $x$-axis
$\Rightarrow 2\times 4-1+\lambda (3\times 4+2)=0$

$\Rightarrow \lambda =-\frac{1}{2}$