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) / (3β3) = (i - j - k) / β3
- Step 1: a Γ b = | i, j, k; 2, 1, 1; 1, -1, 2 |.
- Step 2: i(2 - (-1)) - j(4 - 1) + k(-2 - 1) = 3 i - 3 j - 3 k = 3(i - j - k).
- Step 3: Unit vector = (i - j - k) / sqrt(1 + 1 + 1) = (i - j - k) / β3.
Practise more Vectors.
Free questions with an explanation for every one, and full timed WBJEE mock tests.