First slide

Planes in 3D

Question

Consider the planes 3x-6y+22+5=0 and 4x-12y+32=3.Theplane 67x-162y+47z+44=0 bisects the angle between the given planes which

Moderate

A

contains origin
B

is acute
C

is obtuse
D

none of these

Solution

3x-6y+22+5=0-------- (i)
-4x+12y-32+3=0 --------(ii)
Bisector $\frac{3 x - 6 y + 2 z + 5}{\sqrt{9 + 36 + 4}} = \pm \frac{- 4 x + 12 y - 3 z + 3}{\sqrt{16 + 144 + 9}}$
The plane which bisects the angle between the planes that contains the origin.
13(3x -6y+22 + 5) =7 (4x+ 12y-3z + 3)
67x - 162y + 47z + 44=0 ----------(iii)
Further, 3 x (-4) + (-6) (12) + 2 x (-3) < 0
Hence, the origin lies in the acute angle.

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