The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is
$\frac{1}{7}(3\hat i + 6\hat j - 2\hat k)$
$\frac{1}{7}(3\hat i + 6\hat j + 2\hat k)$
$\frac{1}{{49}}(3\hat i + 6\hat j - 2\hat k)$
$\frac{1}{{49}}(3\hat i - 6\hat j + 2\hat k)$
The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is
Resultant of vectors $\overrightarrow A $ and $\overrightarrow B $
$\overrightarrow R = \overrightarrow A + \overrightarrow B = 4\hat i + 3\hat j + 6\hat k - \hat i + 3\hat j - 8\hat k$
$\overrightarrow R = 3\hat i + 6\hat j - 2\hat k$
$\hat R = \frac{{\overrightarrow R }}{{|\vec R|}} = \frac{{3\hat i + 6\hat j - 2\hat k}}{{\sqrt {{3^2} + {6^2} + {{( - 2)}^2}} }} = \frac{{3\hat i + 6\hat j - 2\hat k}}{7}$
$\overrightarrow R = \overrightarrow A + \overrightarrow B = 4\hat i + 3\hat j + 6\hat k - \hat i + 3\hat j - 8\hat k$
$\overrightarrow R = 3\hat i + 6\hat j - 2\hat k$
$\hat R = \frac{{\overrightarrow R }}{{|\vec R|}} = \frac{{3\hat i + 6\hat j - 2\hat k}}{{\sqrt {{3^2} + {6^2} + {{( - 2)}^2}} }} = \frac{{3\hat i + 6\hat j - 2\hat k}}{7}$
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