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Question

The plane through the intersection of the planes x+y+z=1 and 2x+3yz+4=0 and parallel to y-axis also passes through the point:

A
(3,0,1)
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B
(3,1,1)
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C
(3,2,1)
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D
(3,3,1)
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Solution

The correct option is C (3,2,1)
The family of planes passing through the intersection of given two planes is x+y+z1+λ(2x+3yz+4)=0
(1+2λ)x+(1+3λ)y+(1λ)z+4λ1=0
As the plane is parallel to y-axis,
3λ+1=0λ=13
So, the equation of the plane is
(123)x+(1+13)z73=0
13x+43z73=0x+4z7=0

The equation of plane is x+4z7=0
Hence the plane passes through point (3,2,1)


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