If \(\vec a\) and \(\vec b\), are two non-zero vectors such that \(|\vec a \cdot \vec b| = |\vec a \times \vec b|\), then the angle \(\theta\) between \(\vec a\) and \(\vec b\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{\pi}{4}\)
With \(0 \le \theta \le \pi\), the dot and cross products give
\(|\vec a \cdot \vec b| = |\vec a|\,|\vec b|\,|\cos\theta|\)
\(|\vec a \times \vec b| = |\vec a|\,|\vec b|\sin\theta\)
Equating them and cancelling \(|\vec a|\,|\vec b| \ne 0\):
\(|\cos\theta| = \sin\theta\)
\(|\tan\theta| = 1\)
So \(\theta = \frac{\pi}{4}\) or \(\frac{3\pi}{4}\). Only \(\frac{\pi}{4}\) is among the options.