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If the equation of the plane passing the line of intersection of the planes 2x-7y+4z-3=0,3x-5y+4z+11=0 and the point (-2,1,3) is ax+by+cz-7=0 ,  then the value of 2a+b+c-7 is

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answer is 4.

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Detailed Solution

2x−7y+4z−3+λ3x−5y+4z+11=0which is passing through  (-2,1,3)(-4-7+12-3)+λ(-6-5+12+11)=0-2+λ(12)=0  λ=16 put in equation 15x-47y+28z-7=0ax+by+cz-7=0a=15,b=-47,c=282a+b+c-7  =4.
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If the equation of the plane passing the line of intersection of the planes 2x-7y+4z-3=0,3x-5y+4z+11=0 and the point (-2,1,3) is ax+by+cz-7=0 ,  then the value of 2a+b+c-7 is