Discussion
Let \(\theta\) be the angle between the unit vectors \(\hat{a}\) and \(\hat{b}\). If \(|\hat{a} - \hat{b}| = \frac{\sqrt{3}}{2}\), then the value of \(\cos\theta\) is
Answer: C
\(\cos\theta = \frac{5}{8}\).
For unit vectors, \(|\hat{a}| = |\hat{b}| = 1\), so
\[ \begin{aligned} |\hat{a} - \hat{b}|^{2} &= 1 + 1 - 2\cos\theta \\ \tfrac{3}{4} &= 2 - 2\cos\theta \\ \cos\theta &= \tfrac{5}{8} \end{aligned} \]
Using \(|\hat{a} + \hat{b}|\) instead gives \(\cos\theta = -\frac{5}{8}\), not offered. The option \(\frac{3}{8}\) is \(1 - \cos\theta\).
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