Kinematics Question 30
Question: Two forces $ {{\vec{F}}_1}=5\hat{i}+10\hat{j}-20\hat{k} $ and $ {{\vec{F}}_2}=10\hat{i}-5\hat{j}-15\hat{k} $ act on a single point. The angle between $ {{\vec{F}}_1} $ and $ {{\vec{F}}_2} $ it’s nearly [AMU 1995]
Options:
A) $ 30{}^\circ $
B) $ 45{}^\circ $
C) $ 60{}^\circ $
D) $ 90{}^\circ $
Correct Answer: B $ \cos \theta =\frac{\overrightarrow{F_1}.\overrightarrow{F_2}}{|F_1||F_2|} $ $ =\frac{(5\hat{i}+10\hat{j}-20\hat{k}).(10\hat{i}-5\hat{j}-15\hat{k})}{\sqrt{25+100+400}\sqrt{100+25+225}} $ $ =\frac{50-50+300}{\sqrt{525}\sqrt{350}} $
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Answer:
Solution:
therefore $ \cos \theta =\frac{1}{\sqrt{2}} $
$ \therefore $ $ \theta =45{}^\circ $
