First slide

Planes in 3D

Question

The equations of the plane which passes through (0, 0, 0) and which is equally inclined to the planes
x -y + z- 3 = 0 and x + y+ z + 4= 0 is/are

Moderate

A

y=0
B

x=0
C

x+y=0
D

x+z=0

Solution

The required plane is parallel to the bisector of the given planes.
Bisectors are $\frac{x - y + z - 3}{\sqrt{3}} = \pm \frac{x + y + z + 4}{\sqrt{3}}$
or 2y + 7 =0 and 2x+ 2y + 1 = 0.
Hence, the planes are y=0 and x+y=0.

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