If a → , b → , c → are three non-zero vectors and n ^ is a unit vector perpendicular to c → such that a → = α b → - n ^ , α ≠ 0 and b → · c → = 12 , then c → × a → × b → is equal to:

Question

If a → , b → , c → are three non-zero vectors and n ^ is a unit vector perpendicular to c → such that a → = α b → - n ^ , α ≠ 0 and b → · c → = 12 , then c → × a → × b → is equal to:, 15, 9, 12, 6

MARKS App · Accepted Answer

Given: a → = α b → - n ^ where, α ≠ 0 ⇒ a → · c → = α b → · c → - n ^ · c → ⇒ a → · c → = 12 α - 0 Since, n ^ ⊥ c → ⇒ n ^ · c → = 0 . Now, c → × a → × b → = c → · b → a → - c → · a → b → ⇒ c → × a → × b → = 12 a → - 12 α b → ⇒ c → × a → × b → = 12 a → - α b → ⇒ c → × a → × b → = 12 - n ^ ⇒ c → × a → × b → = 12 - n ^ ⇒ c → × a → × b → = 12 - n ^ ⇒ c → × a → × b → = 12

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