In a triangle P Q R , let a → = Q R → ,   b → = R P → and c → = P Q → . If a → = 3 ,   b → = 4 and a → . c → − b → c → . a → − b → = a → a → + b → , then the value of a → × b → 2 is _______
A. A
a → + b → + c → = 0 ∵ a → . c → − b → c → . a → − b → = a → a → + b → ⇒ − b → + c → ⋅ c → − b → − a → + b → ⋅ a → − b → = a → a → + b → ⇒ c → 2 − b → 2 a → 2 − b → 2 = 3 3 + 4 = 3 7 ⇒ c → 2 = 13 Now, a → + b → = − c → ⇒ a → + b → 2 = − c → 2 ⇒ a → 2 + b → 2 + 2 a → . b → = c → 2 ⇒ 9 + 16 + 2 a → . b → = 13 ⇒ a → · b → = − 6 Now, a → × b → 2 + a → . b → 2 = a → 2 . b → 2 ⇒ a → × b → 2 + 36 = 9 16 ⇒ a → × b → 2 = 108
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