Question

The equation of the plane passing through the intersection of the planes $x + 2y + 3z + 4 = 0$ and $4x + 3y + 2z + 1 = 0$ and the origin is

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

Answer 1

Answer: (B)

$3x + 2y + z = 0$

Answer 2

Equation of plane passing through the intersection of given planes, is

$( x + 2 y + 3 z + 4 ) + \lambda ( 4 x + 3 y + 2 z + 1 ) = 0$ .....(i)

Plane (i) is passing through origin i.e., (0, 0, 0)

∴$4 + \lambda = 0$ ⇒ $\lambda = - 4$

Put the value of $\lambda$ in (i),

$- 15 x - 10 y - 5 z = 0$ ⇒ $3 x + 2 y + z = 0$