Physics - Vectors Question with Solution | TestHub

Finding the angle between the vectors: $\begin{array}{rl}& |\mathrm{A}\times \mathrm{B}|=\sqrt{3}(\mathrm{AB})\\ & |\mathrm{A}||\mathrm{B}|\sin (\theta )=\sqrt{3}|\mathrm{A}||\mathrm{B}|\cos (\theta )\end{array}$ Cancelling both sides we get $\begin{array}{rl}& \sin (\theta )=\sqrt{3}\cos (\theta )\\ & \frac{\sin (\theta )}{\cos (\theta )}=\sqrt{3}\\ & \tan (\theta )=\sqrt{3}\end{array}$ Hence $\theta =60^{\circ }$ Hence the angle between A and B is $60^{\circ }$