Question

The angle $θ$ between the vector $\vec{p}=\hat{i}+\hat{j}+\hat{k}$ and unit vector along $x$-axis is

• A. $cos^{-1}\left(\frac{1}{\sqrt{3}}\right)$
• B. $cos^{-1}\left(\frac{1}{\sqrt{2}}\right)$
• C. $cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$
• D. $cos^{-1}\left(\frac{1}{2}\right)$

Answer 1

Answer: (A)

The angle between
$\vec{p} =\hat{ i }+\hat{ j }+\hat{ k }$
$X$-axis, $\,\,\,x =\hat{ i }$
is given by
$\cos \theta=\frac{ \vec{p} \cdot x }{| \vec{p} \| x |}=\frac{(\hat{ i }+\hat{ j }+\hat{ k })(\hat{ i })}{\sqrt{1^{2}+1^{2}+1^{2}} \cdot \sqrt{1^{2}}}=\frac{1}{\sqrt{3}} $
$\Rightarrow \,\,\, \theta=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$