Question

The equation of the plane containing the line of intersection of the planes $2x - y = 0$and $y - 3z = 0$and perpendicular to the plane $4x + 5y - 3z - 8 = 0$is

• A. $28x - 17y + 9z = 0$
• B. $28x + 17y + 9z = 0$
• C. $28x - 17y + 9x = 0$
• D. $7x - 3y + z = 0$

Answer 1

Answer: (A)

$28x - 17y + 9z = 0$

Answer 2

Equation of plane containing the line of intersection of planes is, $( 2 x - y ) + \lambda ( y - 3 z ) = 0$ ……(i)

Also, plane (i) is perpendicular to $4 x + 5 y - 3 z - 8 = 0$

$\therefore 4 ( 2 ) + 5 ( \lambda - 1 ) - 3 ( - 3 \lambda ) = 0$

$\Rightarrow 14 \lambda = - 3 \Rightarrow \lambda = - \frac { 3 } { 14 }$

Put the value of $\lambda$ in (i), we get $28 x - 17 y + 9 z = 0$ , which is the required plane.