Kinematics Question 431
Question: The unit vector parallel to the resultant of the vectors $ \overrightarrow{A}=4\hat{i}+3j+6\hat{k} $ and $ \overrightarrow{B}=-\hat{i}+3j-8\hat{k} $ it’s
Options:
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 [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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