A) \[\frac{1}{7}(3\widehat{i}+3\widehat{j}-2\widehat{k})\]
B) \[\frac{1}{7}(3\widehat{i}+6\widehat{j}-2\widehat{k})\]
C) \[\frac{1}{49}(3\widehat{i}+6\widehat{j}-2\widehat{k})\]
D) \[\frac{1}{49}(3\widehat{i}-6\widehat{j}+2\widehat{k})\]
Correct Answer: B
Solution :
Resultant of \[\text{\vec{A}}\]and \[\text{\vec{B}}\] is \[\text{\vec{R}}\,\text{= \vec{A}}\,\text{+ \vec{B}}\] \[(4\hat{i}+3\hat{j}+6\hat{k})+(-\hat{i}+3\hat{j}-8\hat{k})\] \[=3\hat{i}+6\hat{j}-2\hat{k}\] and \[|\vec{R}|=\sqrt{({{3}^{2}})+{{(6)}^{2}}+({{2}^{2}})}\] \[=\sqrt{9+36+4}\] \[=\sqrt{49}=7\] Hence, unit vector along resultant \[\hat{n}=\frac{{\vec{R}}}{|\vec{R}|}=\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]
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