Kinematics Question 128
Question: Vector $ \overrightarrow{A} $ makes equal angles with x, y and z axis. Value of it’s components (in terms of magnitude of $ \overrightarrow{A} $ ) will be
Options:
A) $ \frac{A}{\sqrt{3}} $
B) $ \frac{A}{\sqrt{2}} $
C) $ \sqrt{3}A $
D) $ \frac{\sqrt{3}}{A} $
Correct Answer: A Let the components of $ \overrightarrow{A} $ makes angles $ \alpha ,\beta $ and $ \gamma $ with x, y and z axis respectively then $ \alpha =\beta =\gamma $ $ {{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1 $
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Answer:
Solution:
$ \Rightarrow $ $ 3{{\cos }^{2}}\alpha =1 $
therefore $ \cos \alpha =\frac{1}{\sqrt{3}} $
$ \therefore A _{x}=A _{y}=A _{z}=A\cos \alpha =\frac{A}{\sqrt{3}} $
