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AP EAMCET202023 Sep 2020Morning ShiftMathematicsVector AlgebraActual

Number of unit vectors of the form a i ^ + b j ^ + c k ^ , where a , b , c ∈ W is

Options

  1. A2
  2. B4
  3. C3
  4. D6

Correct answer

C. 3

Step-by-step solution

If a i ^ + b j ^ + c k ^ is an unit vector, then a 2 + b 2 + c 2 = 1 ⇒ a 2 + b 2 + c 2 = 1 If a ,   b ,   c ∈ W , then possible values of a , b , c are 1 , 0 , 0 ,   0 , 1 , 0 ,   0 , 0 , 1 ∴ Three unit vectors in the form of a i ^ + b j ^ + c k ^ ,   where a ,   b ,   c ∈ W

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