Question

The angle between two unit vectors \(\vec{A}\) and \(\vec{B}\) is \(60^\circ\). The value of \(|\vec{A} - \vec{B}|\) is

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{1}{4}\)
• D. \(1\)
• E. \(\frac{1}{8}\)

Hint:

For unit vectors: use dot product formula directly.

Answer 1

The Correct Option is D

Concept: \[ |\vec{A} - \vec{B}|^2 = |\vec{A}|^2 + |\vec{B}|^2 - 2\vec{A}\cdot\vec{B} \]

Step 1: Substitute values.
\[ |\vec{A}| = |\vec{B}| = 1,\quad \vec{A}\cdot\vec{B} = \cos 60^\circ = \frac{1}{2} \]

Step 2: Compute.
\[ |\vec{A} - \vec{B}|^2 = 1 + 1 - 2\cdot\frac{1}{2} = 1 \] \[ |\vec{A} - \vec{B}| = 1 \]