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Question

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


A

20x+23y+26z69=0

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B

31x+45y+49z+52=0

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C

8x+5y+2z69=0

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D

4x+5y+6z7=0

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Solution

The correct option is A

20x+23y+26z69=0


Explanation for the correct option:

Given, equation of planes are

x+y+z=6

2x+3y+4z+5=0

Equation of plane passing through intersection of given plane is,

L1+λL2=0

x+y+z6+λ(2x+3y+4z+5)=0

it also passes through (1,1,1)

1+1+1+6+λ(2+3+4+5)=0

λ=314
the required plane is,

14(x+y+z6)+3(2x+3y+4z+5)=0

20x+23y+26z69=0

Hence, Option ‘A’ is Correct.


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