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Passage: Let a , b , c , a + b , b + c , a + b + c be unit vectors. Question: What is the angle between a and b ?

Options

  1. A6
  2. B4
  3. C2
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

Given | a | = 1 , | b | = 1 , and | a + b | = 1 . Squaring the magnitude of a + b , we get: | a + b |^2 = | a |^2 + | b |^2 + 2| a || b | Substituting the given values: 1^2 = 1^2 + 1^2 + 2(1)(1) 1 = 2 + 2 2 = -1 = - 1 2 = 2 3 Answer: 2 3

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