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A straight line L cuts the sides A B , A C , A D of a parallelogram A B C D at B 1 , C 1 , D 1 respectively. If A B → 1 = λ 1 A B → ,   A D → 1 = λ 2 A D → and A C → 1 = λ 3 A C → , then 1 λ 3 is equal to

Options

  1. A1 λ 1 + 1 λ 2
  2. B1 λ 1 - 1 λ 2
  3. C- λ 1 + λ 2
  4. Dλ 1 + λ 2

Correct answer

A. 1 λ 1 + 1 λ 2

Step-by-step solution

Let position vector of A , B , D are o → , b → , d → respectively A B → 1 = λ 1 A B → = λ 1 b → A D → 1 = λ 2 A D → = λ 2 d → A C → 1 = λ 3 A C → = λ 3 b → + d → ∵ B 1 , C 1 , D 1 are collinear B 1 C 1 → = λ 3 - λ 1 b → + λ 3 d → B 1 D 1 → = - λ 1 b → + λ 2 d → ⇒ λ 3 - λ 1 - λ 1 = λ 3 λ 2 ⇒ λ 3 λ

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