The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$.

Solution

$\begin{aligned}& \mathrm{B} \cos \theta=\frac{\mathrm{B}}{2} \\ & \Rightarrow \theta=60^{\circ}\end{aligned}$ So, angle between $\overrightarrow{\mathrm{A}} \& \overrightarrow{\mathrm{B}}$ is $90^{\circ}+60^{\circ}=150^{\circ}$

Hence, the correct answer is 150.