Question

The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $2x + 3y - z + 4 = 0$and parallel to x-axis is

• A. $y - 3z - 6 = 0$
• B. $y - 3z + 6 = 0$
• C. $y - z - 1 = 0$
• D. $y - z + 1 = 0$

Answer 1

Answer: (B)

$y - 3z + 6 = 0$

Answer 2

Equation of plane passing through intersection of given planes is, $( x + y + z - 1 ) + \lambda ( 2 x + 3 y - z + 4 ) = 0$ …..(i)

Plane (i) is parallel to x-axis, then $( 1 + 2 \lambda ) 1 = 0$

⇒ $\lambda = - \frac { 1 } { 2 }$

Put the value of $\lambda$ in (i), we get $y - 3 z + 6 = 0$, which is the required plane.