Kinematics Question 439
Question: Obtain the directions of vector $ (\vec{A}-\vec{B}), $ if $ \vec{A}=2\hat{i}+3\hat{j}=\hat{k},\vec{B}=2\hat{i}+2\hat{j}+3\hat{k} $
Options:
A) $ 0,\frac{1}{\sqrt{5}},\frac{-2}{\sqrt{5}} $
B) $ 0,\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}} $
C) 0, 0, $ \frac{1}{\sqrt{5}} $
D) None of these
Correct Answer: A [a] $ (\vec{A}-\vec{B})=\sqrt{1+4}=\sqrt{5} $ $ (\vec{A}-\vec{B})=2\hat{i}+3\hat{j}+\hat{k}-2\hat{i}-2\hat{j}-3\hat{k} $ $ =\hat{j}-2\hat{k} $ $ |\vec{A}-\vec{B}|=\sqrt{1+4}=\sqrt{5} $ Direction cosine $ =\frac{0}{\sqrt{5}},\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}} $
i.e., $ =0,\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}} $ .
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