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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

Let a → , b → and c → be three vectors such that a → = 2 , b → = 1 and c → = 3 . If the projection of b → along a → is double of the projection of c → along a → and b → , c → are perpendicular to each other, then the value of a → - b → + 2 c → 2 2 is equal to

Options

  1. A41
  2. B14
  3. C14
  4. D20.5

Correct answer

D. 20.5

Step-by-step solution

Given, b → ⋅ c → = 0 b → ⋅ a ^ = 2 c → ⋅ a ^ ⇒ b → ⋅ a → = 2 c → ⋅ a → So, a → - b → + 2 c → 2 = a → 2 + b → 2 + 4 c → 2 - 2 a → ⋅ b → - 4 b → ⋅ c → + 4 a → ⋅ c → a → - b → + c → 2 2 = 4 + 1 + 36 2 = 20 . 5

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