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Question

A plane which bisects the angle between the two given planes 2xy+2z4=0 and x+2y+2z2=0, passes through the point :

A
(1,4,1)
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B
(2,4,1)
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C
(2,4,1)
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D
(1,4,1)
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Solution

The correct option is C (2,4,1)
Equation of angle bisectors are
2xy+2z422+(1)2+22=±x+2y+2z212+(2)2+22

Taking positive sign, we get
x3y2=0 ...(1)
Taking negative sign, we get
3x+y+4z6=0 ...(2)

Now by putting all the given options in the equation (1) and (2), we find that
(2,4,1) satisfies the equation (2)

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