Question

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

• A. $y - 3z + 6 = 0$
• B. $3y - z + 6 = 0$
• C. $y + 3z + 6 = 0$
• D. $3y - 2z + 6 = 0$

Answer 1

Answer: (A)

$y - 3z + 6 = 0$

Answer 2

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

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

or $( 1 + 2 \lambda ) x + ( 1 + 3 \lambda ) y + ( 1 - \lambda ) z + 4 \lambda - 1 = 0$

Since the plane parallel to x-axis,

$\therefore$ $1 + 2 \lambda = 0 \Rightarrow \lambda = - \frac { 1 } { 2 }$

Hence, the required equation will be $y - 3 z + 6 = 0$ .