Mathematics

Problem

Let

\mathbf{a}

and

\mathbf{b}

be two unit vectors. If the vectors

\mathbf{c} = \mathbf{a} + 2\mathbf{b}

and

\mathbf{d} = 5\mathbf{a} - 4\mathbf{b}

are perpendicular to each other, then the angle between

\mathbf{a}

and

\mathbf{b}

is a.

\frac{\pi}{6}

\frac{\pi}{2}

\frac{\pi}{3}

\frac{\pi}{4}