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Let p → = 2 i ^ + j ^ - 2 k ^ , q → = i ^ + j ^ . If r → is a vector such that p → . r → = r → , r → - p → = 2 2 and the angle between p → × q → and r → is π 6 , then the value of p → × q → × r → is equal to

Options

  1. A3 2
  2. B1 2
  3. C3 3 2
  4. D3

Correct answer

A. 3 2

Step-by-step solution

p → × q → × r → = p → × q → r → sin ⁡ 30 o = | p → × q → | | r → | 1 2 … 1 p → × q → = i ^ j ^ k ^ 2 1 - 2 1 1 0 = 2 i ^ - 2 j ^ + k ^ ⇒ p → × q → = 3 Given, r → - p → 2 = 8 ⇒ r → 2 + p → 2 - 2 r → . p → = 8 ⇒ r → 2 + 9 - 2 r → = 8 ⇒ r → = 1 from 1 , p → × q → × r → = 3 2

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