Kinematics Question 2
Question: If $ \overrightarrow{A}=4{i}-3\hat{j} $ and $ \overrightarrow{B}=6\hat{i}+8\hat{j} $ then magnitude and direction of $ \overrightarrow{A}+\overrightarrow{B} $ will be
Options:
A) $ 5,{{\tan }^{-1}}(3/4) $
B) $ 5\sqrt{5},{{\tan }^{-1}}(1/2) $
C) $ 10,{{\tan }^{-1}}(5) $
D) $ 25,{{\tan }^{-1}}(3/4) $
Correct Answer: B $ \overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+6\hat{i}+8\hat{j}=10\hat{i}+5\hat{j} $ $ |\overrightarrow{A}+\overrightarrow{B}|=\sqrt{{{(10)}^{2}}+{{(5)}^{2}}} $ $ =5\sqrt{5} $ $ \tan \theta =\frac{5}{10}=\frac{1}{2} $
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Answer:
Solution:
$ \Rightarrow $ $ \theta ={{\tan }^{-1}}( \frac{1}{2} ) $
