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JEE Main202122 Jul 2021Morning ShiftMathematicsVector AlgebraActual

Let three vectors a → , b → and c → be such that a → × b → = c → , b → × c → = a → and | a → | = 2 . Then which one of the following is not true?

Options

  1. Aa → × ( ( b → + c → ) × ( b → - c → ) ) = 0 →
  2. BProjection of a → on ( b → × c → ) is 2
  3. Ca → b → c → + c → a → b → = 8
  4. D| 3 a → + b → - 2 c → | 2 = 51

Correct answer

D. | 3 a → + b → - 2 c → | 2 = 51

Step-by-step solution

The first option is a → × b → + c → × b → - c → = a → × b → × b → - b → × c → + c → × b → - c → × c → But, we know that b → × b → = 0 = c → × c → = a → × c → × b → - b → × c → Given, b → × c → = a → ,     ⇒ c → × b → = - a → = a → × - a → - b

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