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JEE Main20206 Sep 2020Morning ShiftMathematicsVector AlgebraActual

If a → and b → are unit vectors, then the greatest value of 3 | a → + b → | + | a → - b → | is

Correct answer

4

Step-by-step solution

Let angle between a →   and   b → = α . So, 3 | a → + b → | + | a → - b → | = 3 2 + 2 cosα + 2 - 2 cosα = 3 2 × 2 cos 2 α 2 + 2 × 2 sin 2 α 2 = 2 3 cos α 2 + sin α 2 As α ∈ 0 , π ⇒ α 2 ∈ 0 , π 2 So, given expression is = 2 3 cos α 2 + sin α 2 Thus, maximum value is = 2 3 2 + 1 2 = 2 × 2 = 4

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