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Question

Find the equation of the plane which passes through a1x+b1x+c1z+d1=0, a2x+b2x+c2z+d2=0 and which is parallel to the line xαl=yβm=zγn

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Solution

The equation of plane passing through a1x+b1y+c1z+d1=0,a2x+b2y+c2z+d2=0 will be (a1x+b1y+c1z+d1)+λ(a2x+b2y+c2z+d2)=0
(a1+λa2)x+(b1+λb2)y+(c1+λc2)z+(d1+λd2)=0
Since this plane is parallel to xαl=yβm=zγn
(a1+λa2)l+(b1+λb2)m+(c1+λc2)n=0λ=a1l+b1m+c1na2l+b2m+c2n
The plane equation is (a1x+b1y+c1z+d1)(a1l+b1m+c1n)(a2l+b2m+c2n)(a2x+b2y+c2z+d2)=0

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