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Question

Consider the planes 3x6y+2z+5=0 and 4x12y+3z=3. The plane 67x162y+47z+44=0 bisects the angle between the given planes which-

A
Contains origin
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B
Is acute
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C
Is obtuse
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D
None of these
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Solution

The correct options are
B Contains origin
C Is acute
For 3x6y+2z+5=0 and 4x+12y3z+3=0 bisector are
3x6y+2z+59+36+4=±4x+12y3z+316+144+9
The plane which bisects the angle between the plane that contains the origin
13(3x6y+2z+5)=7(4x+12y3z+3)67x162y+47z+44=0
Further 3×(4)+(6)×12+2×(3)<0
Hence, the origin lies in the acute angle.

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