Practice question · Select all that apply
Let u = (1, 2, -2). Select every vector below that is orthogonal to u.
Hints
- Dot each candidate with u and keep only the ones giving exactly zero.
- The five dot products are 0, 0, 1, 0 and -1.
Show the answer
- B. (2, 0, 1)
- D. (2, -1, 0)
- E. (0, 1, 1)
Why
(2, 0, 1) gives 2 + 0 - 2 = 0; (2, -1, 0) gives 2 - 2 + 0 = 0; (0, 1, 1) gives 0 + 2 - 2 = 0. The other two give 1 and -1, so their angles with u are merely near a right angle, not equal to one. In space a whole plane of vectors is orthogonal to u, so several answers being correct is expected.
Practise Dot Product and Angles
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