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Question

The equation of the plane passing through the intersection of the planes 2x – 5y + z = 3 and x + y + 4z = 5 and Parallel to the plane x + 3y + 6z = 1 is x + 3y + 6z = k, where k is

A
5
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B
3
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C
7
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D
2
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Solution

The correct option is B 3
Equation of plane passing through the intersection on the planes
2x5y+z=3 and x+y+4z=5 is
(2x5y+z3)+λ(x+y+4z)=0
(2+λ)x+(5+λ)y+(1+4λ)35λ=0 .........(i)
Which is parallel to the plane x+3y+6z=1.
Then, 2+λ1=5+λ3=1+4λ6
λ=112
From Eq.(i),
72x212y21z+492=0x+3y+6z=7
Hence, k=7

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