Question

Equation of the plane passing through the point of intersection of x+2y+=0 and 2x+y=0 and which is perpendicular to 5x+6z=0

• A. x=0
• B. y=0
• C. z=0
• D. x+y=0
• E. x+z=0

Answer 1

Answer: (A), (B)

The correct options are
A x=0
B y=0

$E{q}^n.$ of plane passing through point of intersection

$\Rightarrow (x+2y)+\lambda (2x+y)=0\Rightarrow (1+2\lambda )x+(2+\lambda )y=0...\left(1\right)$

Since,this plane is $\perp$ to plane $5x+6z=0$

$a_1{a}_2+b_1{b}_2+c_1{c}_2=0$

$5(1+2\lambda )\ne 0$ $5+10\lambda =0$

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

$E{q}^n.$ of plane : $(1+2\lambda )x+(2+\lambda )y=0$

$[1+2(\frac{-1}{2}\left)\right]x+\left[2\frac{-1}{2}\right]y=0$

$(1-1)x+\frac{3}{2}y=0$

$x=0,$ $y=0$