3-1.Vectors
medium

$\overrightarrow A = 3\hat i + \hat j + 2\hat k$ અને $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$ ,બંનેને લંબ દિશામાંનો એકમ સદિશ મેળવો.

A$ + \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$
B$ - \frac{1}{{\sqrt 3 }}(\hat i - \hat j - \hat k)$
C$(a)$ અને $(b)$ બંને
Dએકપણ નહીં.

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 $\hat n = \pm \frac{1}{{\sqrt 3 }}(\hat i – \hat j – \hat k)$
Standard 11
Physics

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