If A = 2 i + 3 j - k and B = - i + 3 j + 4 k a unit vector perpen… - Vidyadip

MCQ

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ a unit vector perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ will be

A
$ + \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$
B
$ - \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$
✓
Both $(a)$ and $(b)$
D
None of these

✓

Answer

Correct option: C.

Both $(a)$ and $(b)$

c
(c) $\hat n = \frac{{\overrightarrow A \, \times \overrightarrow B }}{{|\overrightarrow A \, \times \overrightarrow B |}} = \frac{{8\hat i - 8\hat j - 8\hat k}}{{8\sqrt 3 }} = \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$

There are two unit vectors perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ they are $\hat n = \pm \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$

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