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The angle between the vectors a = i +2 j +2 k and b = i +2 j -2 k is

Options

  1. A⁻¹(1 / 9)
  2. B⁻¹(8 / 9)
  3. C⁻¹(1 / 9)
  4. D⁻¹(8 / 9)

Correct answer

A. ⁻¹(1 / 9)

Step-by-step solution

The angle between two vectors a and b is given by the formula = a b | a | | b | . Given a = i + 2 j + 2 k and b = i + 2 j - 2 k . Calculate the dot product a b = (1)(1) + (2)(2) + (2)(-2) = 1 + 4 - 4 = 1 . Calculate the magnitudes | a | = 1^2 + 2^2 + 2^2 = 1 + 4 + 4 = 9 = 3 . Calculate the magnitude | b | = 1^2 + 2^2 + (-2)^2 = 1 + 4 + 4 = 9 = 3 . Substitute these values into the formula: = 1 3 3 = 1 9 . Therefore, = ⁻¹(1/9) . Answer: ⁻¹(1 / 9)

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