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AP EAMCET201825 Apr 2018Morning ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ + j ^ - 2 k ^ and b → = i ^ + j ^ be two vectors. c ¯ is a vector such that a → · c → = c → and c → - a → = 2 2 . If the angle between a → × b → and c → is 30 ° , then a → × b → × c → is equal to

Options

  1. A3 2
  2. B2 3
  3. C2
  4. D3 2

Correct answer

A. 3 2

Step-by-step solution

Given, a → = 2 i ^ + j ^ - 2 k ^ a → = 4 + 1 + 4 = 3 Now, a → × b → = i ^ j ^ k ^ 2 1 - 2 1 1 0 = 2 i ^ - 2 j ^ + k ^ Then, a → × b → = 4 + 4 + 1 = 3 Now, we have 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 Now, a → × b → × c &#8

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