If a x + 13 y + b z + c = 0 is a plane through the line of intersection of 2 x + 3 y - z + 1 = 0 , x + y - 2 z + 3 = 0 and is perpendicular to the plane 3 x - y - 2 z = 4 , then the value of 2 a + 3 b + 4 c is equal to

Question

If a x + 13 y + b z + c = 0 is a plane through the line of intersection of 2 x + 3 y - z + 1 = 0 , x + y - 2 z + 3 = 0 and is perpendicular to the plane 3 x - y - 2 z = 4 , then the value of 2 a + 3 b + 4 c is equal to, - 12, 12, 10, - 10

MARKS App · Accepted Answer

Equation of the plane through the line of intersection of given 2 planes is 2 x + 3 y - z + 1 + λ x + y - 2 z + 3 = 0 2 + λ x + 3 + λ y - 1 + 2 λ z + 1 + 3 λ = 0 ∵ it is perpendicular to 3 x - y - 2 z = 4 6 + 3 λ - 3 - λ + 4 λ + 2 = 0 6 λ + 5 ⇒ λ = - 5 6 7 x + 13 y + 4 z - 9 = 0 On comparing a = 7 , b = 4 , c = - 9

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