First slide

Planes in 3D

Question

The equation of the plane through the intersection of the planes x+2y+3z-4=0 and 4x+3y+22+ 1 = 0 and passing through the origin is

Moderate

A

17x+14y+11z=0
B

7x+4y+z=0
C

x+14y+11z=0
D

17x+y+z=0

Solution

Any plane through the given planes is $x + 2 y + 3 z - 4 + λ (4 x + 3 y + 2 z + 1) = 0$
It passes through (0, 0, 0). Therefore, $- 4 + λ = 0$
or, $λ = 4$
Therefore, the required plane is x + 2y + 3z + 4(4x + 3y + 2z) = 0 or 17x + 14y + 11z=0.

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