The angle between two lines whose direction cosines are \(\displaystyle\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\) and \(\displaystyle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{\pi}{3}\)
For lines with direction cosines \(l_1, m_1, n_1\) and \(l_2, m_2, n_2\), the angle \(\theta\) between them is given by
\(\cos\theta = |l_1l_2+m_1m_2+n_1n_2|\)
\( \displaystyle \cos\theta = \frac{1}{\sqrt{2}}\cdot\frac{1}{\sqrt{2}}+0\cdot\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\cdot 0 = \frac{1}{2} \)
\( \displaystyle \theta = \frac{\pi}{3} \)