Question

$\overrightarrow{A}\times \overrightarrow{B}=\frac{1}{2}AB,$ what is the angle between $A$ and $B?$

• (A) Zero
• (B) ${30}^{\circ }$
• (C) ${60}^{\circ }$
• (D) ${90}^{\circ }$

Answer 1

The Correct Option is C

Explanation:
Using Dot Product principle: $A\times B=AB\cos (\mathrm{\$})$Here, $\mathrm{\$}$, means the angle between vector $A$ and $B$Angle of arbitrary vectors $A,B$, is defined in range $(0^{\circ },{180}^{\circ })$Then, factor $AB$ dissolved on both sides of equation. We will get $\cos (\mathrm{\$})=\frac{1}{2}$Finally referring to the above range, you can get only one answer:${60}^{\circ }$Hence, the correct option is (C).