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Question

Let the plane passing through the point (1,0,2) and perpendicular to each of the planes 2x+yz=2 and xyz=3 be ax+by+cz+8=0. Then the value of a+b+c is equal to

A
3
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B
5
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C
8
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D
4
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Solution

The correct option is D 4
Given equation of plane is ax+by+cz+8=0
Since it passes through the point(1,0,2)
a2c+8=0
a+2c8=0 (1)
and ax+by+cz+8=0 is perpendicular to 2x+yz=2 and xyz=3
2a+bc=0 (2)
abc=0 (3)
From (1),(2) and (3), we get
a=2,b=1 and c=3
a+b+c=4

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