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# Engineering

If the equation of the plane passing through the line of intersection of the planes 2x-7y+4z-3=0,3x-5y+4z+11=0 and the point \left ( -2,1,3 \right ) is ax+by+cz-7=0, then the value of 2a+b+c-7 is ___________.
Option: 1 4
Option: 2 8
Option: 3 12
Option: 4 16

Answers (1)
S Suraj Bhandari

 

Required plane is

P_{1}+\lambda P _{2}=(2+3 \lambda) x -(7+5 \lambda) y+(4+4 \lambda) z -3+11 \lambda=0 ;

which is satisfied by the point (-2,1,3).

Hence, \lambda=\frac{1}{6}

Thus, plane is 15 x -47 y +28 z -7=0

So, 2 a+b+c-7=4

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