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JEE Main202127 Jul 2021Morning ShiftMathematicsVector AlgebraActual

Let a → = i ^ + j ^ + k ^ , b → and c → = j ^ - k ^ be three vectors such that a → × b → = c → and a → · b → = 1 . If the length of projection vector of the vector b → on the vector a → × c → is l , then the value of 3 l 2 is equal to _____.

Correct answer

0

Step-by-step solution

Given, a → × b → = c → ⇒ a → × b → · c → = c → 2 = 1 2 + 1 2 2 = 2 Here, a → × c → = i ^ j ^ k ^ 1 1 1 0 1 - 1 = - 2 i ^ + j ^ + k ^ Projection of b → on a → × c → = ℓ ⇒ b → · a → × c → a → × c → = ℓ ⇒ a → × b → · c → 2 2 + 1 + 1 = ℓ ∴   ℓ = 2 6 ⇒ ℓ 2 = 4 6 So, 3 ℓ 2 = 2

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