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Question

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1) is

A
2x + 3y + 4z = 9
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B
x + y + z = 3
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C
x + 2y + 3z = 6
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D
20x + 23y + 26z = 69
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Solution

The correct option is D 20x + 23y + 26z = 69
Equation of any plane through the line of intersection of the given planes is
2x+3y+4z+5+λ(x+y+z6)=0
It passes through (1,1,1)if(2+3+4+5)+λ(1+1+16)=0λ=143 and the required equation is therefore, 20x + 23y + 26z = 69.

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