If θ is the angle between any two vectors

​$$\vec{a} \text { and } \vec{b} \text {, then }|\vec{a} \times \vec{b}|=|\vec{a} \cdot \vec{b}| \text { when } \theta \text { is: }$$​​

Correct option is B

​$$\begin{aligned}&\bullet \ \text{Dot product:} \quad \vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta \\&\bullet \ \text{Cross product (magnitude):} \quad |\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|\sin\theta \\\\&\text{We are given that:} \\&\quad |\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}| \\\\&\text{Substitute the above formulas:} \\&\quad |\vec{a}||\vec{b}|\sin\theta = |\vec{a}||\vec{b}|\cos\theta \\\\&\text{Canceling } |\vec{a}||\vec{b}| \text{ from both sides (assuming neither is zero):} \\&\quad \sin\theta = |\cos\theta| \\&\textbf{Solve } \sin\theta = \cos\theta: \\&\text{Divide both sides by } \cos\theta \ (\text{assuming } \cos\theta \ne 0): \\&\quad \tan\theta = 1 \Rightarrow \theta = 45^\circ \quad (\text{or } \theta = \frac{\pi}{4} \text{ radians})\end{aligned}$$​​