Find the unit vector perpendicular to both a = 2 i + j + k and b = i - j + 2 k.

Answer and explanation

Correct answer: B. (3 i - 3 j - 3 k) / (3√3) = (i - j - k) / √3

  1. Step 1: a Γ— b = | i, j, k; 2, 1, 1; 1, -1, 2 |.
  2. Step 2: i(2 - (-1)) - j(4 - 1) + k(-2 - 1) = 3 i - 3 j - 3 k = 3(i - j - k).
  3. Step 3: Unit vector = (i - j - k) / sqrt(1 + 1 + 1) = (i - j - k) / √3.

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