If a → , b → and c → are three vectors such that 3 a → + 4 b → + 6 c → = 0 → , a → = 3 , b → = 3 and c → = 4 , then the value of - 864 a → . b → + b → ⋅ c → + c → . a → 6 is equal to

Question

If a → , b → and c → are three vectors such that 3 a → + 4 b → + 6 c → = 0 → , a → = 3 , b → = 3 and c → = 4 , then the value of - 864 a → . b → + b → ⋅ c → + c → . a → 6 is equal to,

MARKS App · Accepted Answer

3 a → + 4 b → = - 6 c → ⇒ 3 a → + 4 b → 2 = 36 c → 2 ⇒ 9 a → 2 + 16 b → 2 + 24 a → . b → = 36 c → 2 ⇒ 81 + 144 + 24 a → . b → = 576 ⇒ a → . b → = 351 24 Similarly, 3 a → + 6 c → = - 4 b → ⇒ 3 a → + 6 c → 2 = 16 b → 2 ⇒ 9 a → 2 + 36 c → 2 + 36 a → . c → = 16 b → 2 ⇒ 81 + 576 + 36 a → . c → = 144 ⇒ a → . c → = - 513 36 And, 6 c → + 4 b → = - 3 a → ⇒ 36 c → | 2 + 16 b → | 2 + 48 b → ⋅ c → = 9 a → 2 ⇒ 576 + 144 + 48 b → . c → = 81 ⇒ b → . c → = - 213 16 Hence, - 864 ( a → . b → + b → . c → + c → . a → ) 6 = - 12636 + 12312 + 11502 6 = 1863

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