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JEE Main202120 Jul 2021Morning ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ + j ^ - 2 k ^ and b → = i ^ + j ^ . If c → is a vector such that a → · c → = | c → | , | c → - a → | = 2 2 and the angle between a → × b → and c → is π 6 , then the value of a → × b → × c → is:

Options

  1. A2 3
  2. B4
  3. C3
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

We have, a → = 3 = a a → · c → = c → = c Now, c → - a → = 2 2 ⇒   c → - a → 2 = 8 ⇒   c 2 + a 2 - 2 c → · a → = 8 ⇒   c 2 + 9 - 2 c = 8 ⇒     c 2 - 2 c + 1 = 0 ⇒   c - 1 2 = 0 ⇒     c = 1 = c → Now, a → × b → = i ^ j ^ k ^ 2 1 - 2 1 1 0 ⇒     a → × b → = 2 i ^ - 2 j ^ + k ^ ⇒     a → × b &#

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