A) \[\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]
B) \[\frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k})\]
C) \[\frac{1}{49}(3\hat{i}+6\hat{j}-2\hat{k})\]
D) \[\frac{1}{49}(3\hat{i}-6\hat{j}+2\hat{k})\]
Correct Answer: A
Solution :
Resultant of vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] \[\overrightarrow{R}=\overrightarrow{A}+\overrightarrow{B}=4\hat{i}+3\hat{j}+6\hat{k}-\hat{i}+3\hat{j}-8\hat{k}\] \[\overrightarrow{R}=3\hat{i}+6\hat{j}-2\hat{k}\] \[\hat{R}=\frac{\overrightarrow{R}}{|\vec{R}|}=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{\sqrt{{{3}^{2}}+{{6}^{2}}+{{(-2)}^{2}}}}=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7}\]
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