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JEE Main20202 Sep 2020Evening ShiftMathematicsVector AlgebraActual

Let the position vectors of points ' A ' and ' B ' be i ^ + j ^ + k ^ and 2 i ^ + j ^ + 3 k ^ , respectively. A point ' P ' divides the line segment A B internally in the ratio λ : 1 λ > 0 . If O is the origin and OB → · OP → - 3 OA → × OP → 2 = 6 then λ is equal to

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Position vector of P is O P → = a → + λ b → λ + 1 ∵    OB → · OP → - 3 | OA → × OP → | 2 = 6 ⇒    b → · a → + λ b → λ + 1 - 3 a → × a → + λ b → λ + 1 2 = 6 ⇒ a → · b → + λ | b → | 2 λ + 1 - 3 λ 2 ( λ + 1 ) 2 | a → × b → | 2 = 6 ⇒    6 + λ . 14 λ + 1 - 3 λ 2 ( &#9

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