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Q.

Consider the lines L1:x12=y1=z+31, L2:x41=y+31=z+32 and the planes P1:7x+y+2z=3, P2:3x+5y6z=4. Let ax+by+cz=d the equation of the plane passing through the point of intersection of lines L1 and L2 and perpendicular to planes P1 and P2. then (a+d)(b+c)=_____

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answer is 29.

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Detailed Solution

The normal to the plane is

i^j^k^712356=16i^+48j^+32k^ 

 h=i^3j^2k^  be The point of intersection of L1 and L2 is given by

2λ+1=μ+4λ=μ3  1=3μ2

So, μ=1;   point of intersection is (5,–2,– 1)

The equation of desired plane isx3y2z=13

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