If the lines L 1 : x - 1 3 = y - λ 1 = z - 3 2 and L 2 : x - 3 1 = y - 1 2 = z - 2 3 are coplanar, then the equation of the plane passing through the point of intersection of L 1 and L 2 which is at a maximum distance from the origin is

Question

If the lines L 1 : x - 1 3 = y - λ 1 = z - 3 2 and L 2 : x - 3 1 = y - 1 2 = z - 2 3 are coplanar, then the equation of the plane passing through the point of intersection of L 1 and L 2 which is at a maximum distance from the origin is, 3 x + 2 y + z = 5, 2 x + 3 y + z = 6, 4 x + 3 y + 5 z = 0, 4 x + 3 y + 5 z = 50

MARKS App · Accepted Answer

∵ L 1 and L 2 are coplanar, hence, - 2 λ - 1 1 3 1 2 1 2 3 = 0 ⇒ λ = 2 Now point of intersection will be P 4 , 3 , 5 ∴ Equation of required plane is 4 x + 3 y + 5 z = 50

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