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3-1.Vectors
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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)$
CBoth $(a)$ and $(b)$
DNone of these
Solution
(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 $\hat n = \pm \frac{1}{{\sqrt 3 }}(\hat i – \hat j – \hat k)$
There are two unit vectors perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ they are $\hat n = \pm \frac{1}{{\sqrt 3 }}(\hat i – \hat j – \hat k)$
Standard 11
Physics
