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JEE Main202331 Jan 2023Morning ShiftMathematicsVector AlgebraActual

Let a → and b → be two vector such that a → = 14 , b → = 6 and a → × b → = 48 . Then a → · b → 2 is equal to _____ .

Correct answer

0

Step-by-step solution

Given, a → = 14 ,   b → = 6   &   a → × b → = 48 Now we know that, a → × b → 2 + a → · b → 2 = a → 2 b → 2 sin 2 θ + a → 2 b → 2 cos 2 θ ⇒ a → × b → 2 + a → · b → 2 = a → 2 b → 2 as   cos 2 θ + sin 2 θ = 1 ⇒ 48 + a → · b → 2 = 14 × 6 ⇒ a → · b → 2 = 84 - 48 = 36 .

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