Question

If the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $q$ and if $|\overrightarrow{a}\times \overrightarrow{b}|=\overrightarrow{a}\cdot \overrightarrow{b}$, Then $q=$

• A. ${60}^0$
• B. ${45}^0$
• C. ${30}^0$
• D. ${120}^0$

Answer 1

Answer: (B)

${45}^0$

We have $|\overrightarrow{a}\times \overrightarrow{b}|=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|sinq$
Since $\overrightarrow{a}\cdot \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|cosq$
$\therefore$ $\sin q=\cos q$
$q={45}^{\circ }$