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