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Manipal MET2010MathematicsVector Algebra

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 30^ , then |( a b ) c | is equal to

Options

  1. A2 3
  2. B3 2
  3. C2
  4. D3

Correct answer

B. 3 2

Step-by-step solution

We have, a c =| c | and | c - a |=2 2 a c =| c | and | c |^2+| a |^2-2( a c )=8 | c |^2+9-2| c |=8 (| c |-1)^2=0 | c |=1 |( a b ) c |=| a b || c | 30^ = 1 2 | a b |= 3 2 [ a b =2 i -2 j + k ]

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