Question

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \( \sqrt{3}\vec{a} - \vec{b} \) to be a unit vector is given by :

• A. \(\pi/6\)
• B. \(\pi/4\)
• C. \(\pi/3\)
• D. \(2\pi/3\)

Hint:

When dealing with unit vectors and magnitudes, always square the vector equation to convert magnitudes into dot products. This leverages the properties \( |\vec{v}|^2 = \vec{v} \cdot \vec{v} \) and \( \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos\theta \) for unit vectors.

Answer 1

The Correct Option is A