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Discussion Forum



1)

 The angle subtended  by the vector   $A=4\hat{i}+3\hat{j}+12\hat{k}$ with the X-axis is 


A) $\cos^{-1}\left(\frac{3}{13}\right)$

B) $\sin^{-1}\left(\frac{3}{13}\right)$

C) $\sin^{-1}\left(\frac{4}{13}\right)$

D) $\cos^{-1}\left(\frac{4}{13}\right)$

Answer:

Option D

Explanation:

 Given ,  $A=4\hat{i}+3\hat{j}+12\hat{k}$

 Also, A= Ax+Ay+Az

 $\Rightarrow$    Ax=4

 The angle subtended by vector A with X- axis is 

$\cos \phi=\frac{A_{x}}{|A|}=\frac{4}{\sqrt{4^{2}+3^{2}+12^{2}}}$

 $\cos \phi=\frac{4}{13}$

$\phi=\cos^{-1}\left(\frac{4}{13}\right)$