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Q.

ABCD is a Parallelagram $A_{1}$ and $B_{1}$ are mid points of sides BC and CD respectively. If ${\bar{AA}}_{1} + {\bar{AB}}_{1} = λ \bar{AC}$ then $2 λ =$

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answer is 3.

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Detailed Solution

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$A b e t h e o r i g i n A B = b, A D = d \Rightarrow \bar{A C} = b + d ∴ A A_{1} = \frac{2 b + d}{2}, A B_{1} = \frac{b + 2 d}{2} \Rightarrow A A_{1} + A B_{1} = \frac{2 b + d}{2} + \frac{b + 2 d}{2} = \frac{3}{2} (b + d) = \frac{3}{2} \bar{A C} \Rightarrow λ = \frac{3}{2} ∴ 2 λ = 3$

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