A) \[\frac{1}{6}\,5\hat{i}-\hat{k}\]
B) \[\frac{1}{\sqrt{35}}(5\hat{i}+3\hat{j}-\hat{k})\]
C) \[\frac{1}{5}(3\hat{j}-5\hat{k})\]
D) \[3\hat{i}+6\hat{j}-6\hat{k}\]
E) None of these
Correct Answer: E
Solution :
Given that, \[a=\hat{i}+2\hat{j}-3\hat{k}\] and \[b=2\hat{i}+4\hat{j}+9\hat{k}\] Now, \[a+b=3\hat{i}+6\hat{j}+6\hat{k}\] \[\therefore \]Unit vector parallel to \[(a+b)=\frac{(a+b)}{|a+b|}\] \[=\frac{3\hat{i}+6\hat{j}+6\hat{k}}{\sqrt{9+36+36}}=\frac{3(\hat{i}+2\hat{j}+2\hat{k})}{\sqrt{81}}\] \[=\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]
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