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

Question

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

MARKS App · Accepted Answer

Required plane is p 1 + λ p 2 = ( 2 + 3 λ ) x - ( 7 + 5 λ ) y + ( 4 + 4 λ ) z - 3 + 11 λ = 0 ; which is satisfied by ( - 2 , 1 , 3 ) . Hence, λ = 1 6 Thus, plane is 15 x - 47 y + 28 z - 7 = 0 So, 2 a + b + c - 7 = 4

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