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JEE Main20209 Jan 2020Evening ShiftMathematicsVector AlgebraActual

Let a → , b → and c → be three vectors such that a → = 3 , b → = 5 , b → ∙ c → = 10 and the angle between b → and c → is π 3 . If a → is perpendicular to the vector b → × c → , then a → × b → × c → is equal to ____________.

Correct answer

0

Step-by-step solution

b → . c → = 10 ⇒ b → c → cos ⁡ π 3 = 10 ⇒ 5 . c → . 1 2 = 10 ⇒ c → = 4 Also, a → . b → × c → = 0 a → × b → × c → = a → b → × c → sin ⁡ π 2 ⇒ 3 × b → c → sin ⁡ π 3 × 1 ⇒ 3 × 5 × 4 × 3 2 = 30

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