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Question

The equation of the plane containing the line 2x - 5y + z = 3, x + y + 4z = 5 and parallel to the plane x + 3y + 6z = 1, is 


A
2x +6y +12z =13
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B
x +3y +6z = -7
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C
x +3y +6z =7
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D
2x +6y +12z = -13
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Solution

The correct option is C x +3y +6z =7
Equation of the required plane is 2x5y+z3+λ(x+y+4z5)=0x(2+λ)+y(λ5)+z(4λ+1)35λ=0

Since, this plane is parallel to x+3y+6z=1, we have
λ+21=λ53=4λ+16

Solving, we get λ=112

Substituting for λ in the plane's equation,

7x221y221z+492=0x+3y+6z7=0

Mathematics

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