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JEE Main202329 Jan 2023Morning ShiftMathematicsVector AlgebraActual

Let a → , b → and c → be three non-zero non-coplanar vectors. Let the position vectors of four points A ,   B ,   C and D be a → - b → + c → ,    λ a → - 3 b → + 4 c → , - a → + 2 b → - 3 c → and 2 a → - 4 b → + 6 c → respectively. If A B → , A C → and A D → are coplanar, then λ is

Correct answer

2

Step-by-step solution

Given, a → , b → and c → be three non-zero non-coplanar vectors, Also the position vectors of four points A ,   B ,   C and D be a → - b → + c → ,    λ a → - 3 b → + 4 c → , - a → + 2 b → - 3 c → and 2 a → - 4 b → + 6 c → respectively, So, A B → = ( λ - 1 ) a → - 2 b → + 3 c → A C → = - 2 a → + 3 b → - 4 c → A D → = a → - 3 b → + 5

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