A) \[\frac{1}{7}\,(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})\]
B) \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\]
C) \[\frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}}\]
D) \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-\mathbf{j}+8\mathbf{k})\]
Correct Answer: A
Solution :
Resultant vector \[=(2\mathbf{i}+4\mathbf{j}-5\mathbf{k})+(\mathbf{i}+2\mathbf{j}+3\mathbf{k})=3\mathbf{i}+6\mathbf{j}-2\mathbf{k}\] Unit vector \[=\frac{3\mathbf{i}+6\mathbf{j}-2\mathbf{k}}{\sqrt{9+36+4}}=\frac{1}{7}(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})\].
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