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Question

The equation of the plane through the intersection of the plane 3x-y+2z=0, x+y+z-2=0 and the point (2,2,1) is


A

7x+5y+4z+8=0

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B

7x+5y+4z-8=0

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C

7x-5y+4z-8=0

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D

None of these

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Solution

The correct option is C

7x-5y+4z-8=0


Form the equation of the plane based on given information

Equation of the plane through the intersection of the given planes is given by

3x-y+2z-4+λ(x+y+z-2)=0...(i) where λ

The point (2,2,1) lies on this plane. Hence it must satisfy the equation (i)

Substituting the co-ordinates in equation (i) we get

3(2)-2+2(1)-4+λ(2+2+1-2)=0

3λ=-2

λ=-23

Re-substituting this value of λ in equation (i) we get

3x-y+2z-4-23x+y+z-2=0

9x-3y+6z-12-2x-2y-2z+4=0

7x-5y+4z-8=0

Hence, option (C) 7x-5y+4z-8=0, is the correct answer.


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