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
\((a) \frac{1}{7}(3\hat{i} + 6\hat{j} - 2\hat{k}) \quad (b) \frac{1}{7}(3\hat{i} + 6\hat{j} + 2\hat{k}) (c) \frac{1}{49}(3\hat{i} + 6\hat{j} - 2\hat{k}) \quad (d) \frac{1}{49}(3\hat{i} - 6\hat{j} + 2\hat{k})\)
Text Solution
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Resultant of vectors \vec{A} and \vec{B}
\vec{R} = \vec{A} + \vec{B} = 4\hat{i} + 3\hat{j} + 6\hat{k} - \hat{i} + 3\hat{j} - 8\hat{k}
\vec{R} = 3\hat{i} + 6\hat{j} - 2\hat{k}
\(\hat{R} = \frac{\vec{R}}{|\vec{R}|} = \frac{3\hat{i} + 6\hat{j} - 2\hat{k}}{\sqrt{3^2 + 6^2 + (-2)^2}} = \frac{3\hat{i} + 6\hat{j} - 2\hat{k}}{7}\)
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