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Paragraph: Let a vector a =4 i -8 j + k make angles , , with the positive directions of x, y, z axes respectively. Question: What is 2 + 2 equal to?

Options

  1. A- 32 81
  2. B- 16 81
  3. C16 81
  4. D32 81

Correct answer

A. - 32 81

Step-by-step solution

= a₂ a₁^2+a₂^2+a₃^2 = -8 9 = a₃ a₁^2+a₂^2+a₃^2 = 1 9 2 + 2 =2 ^2 -1+2 ^2 -1=2 ( -8 9 )^2+2 ( 1 9 )^2-2= 128 81 + 2 81 -2= -32 81 .

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