The equation of a plane through the line of intersection of 2x+3y+z-1=0 and x+5y-2z+7=0 and parallel to the line y=0=z is _______________

Dear Tapasranjan Das

equation of a plane through the line of intersection of 2x+3y+z-1=0 and x+5y-2z+7=0  is

2x+3y+z-1+ λ(x+5y-2z+7)=0

(2+λ)x +(3+5λ)y +(1-2λ)z -1-7λ=0

it is parallel to x axix so

(2+λ).1 +(3+5λ).0 +(1-2λ).0 =0

 2+λ=0

λ=-2

so equation of plane is   -7y +5z +13=0

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