Question

If $|\overline{a}\times \overline{b}|=|\overline{a}\cdot \overline{b}|$, then the angle between $\overline{a}$ and $\overline{b}$ is:

• A. ${90}^0$
• B. ${60}^0$
• C. $0^0$
• D. ${45}^0$

Answer 1

Answer: (D)

${45}^0$

$|\overline{a}\times \overline{b}|=|\overline{a}.\overline{b}|$
$|\overline{a}||\overline{b}|$$sin\theta$=$|\overline{a}||\overline{b}|$$cos\theta$
The above expression reduces to $cos\theta =sin\theta$
where $\theta$ is angle between $a$ and $b$
value of $\theta$ is ${45}^0$