Question

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

• A. $x + y + z = 0$
• B. $17 x + 14 y + 11 z = 0$
• C. $7 x + 4 y + z = 0$
• D. $17 x + 14 y + z = 0$

Answer 1

Answer: (B)

$17 x + 14 y + 11 z = 0$

Answer 2

Any plane through the given planes is

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

It passes through (0, 0, 0)

∴ $- 4 + k = 0$ = k = 4

∴Required plane is $( x + 2 y + 3 z - 4 ) + 4 ( 4 x + 3 y + 2 z + 1 ) = 0$

⇒ $17 x + 14 y + 11 z = 0$