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
Solution :
\[\overrightarrow{A}+\overrightarrow{B}=4\hat{i}-3\hat{j}+6\hat{i}+8\hat{j}\,\,=10\hat{i}+5\hat{j}\] \[|\overrightarrow{A}+\overrightarrow{B}|\,=\,\sqrt{{{(10)}^{2}}+{{(5)}^{2}}}\] \[=\,5\sqrt{5}\] \[\tan \theta =\frac{5}{10}=\frac{1}{2}\] \[\Rightarrow \]\[\theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\]You need to login to perform this action.
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