Question

What is the angle between $(\hat{i}+\hat{j}+\hat{k})$ and $\hat{i}$?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Answer 1

The correct option is D $co{s}^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\cos \theta =\frac{(\hat{i}+\hat{j}+\hat{k})}{\left|\right(\hat{i}+\hat{j}+\hat{k}\left)\right|\left|\hat{i}\right|}$

$\cos \theta =\frac{1}{\sqrt{3}\times \sqrt{1}}=\frac{1}{\sqrt{3}}$

Hence, $\theta ={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$