Question

If $\left|\vec{a}\right| = 5$, $ \left|\vec{b}\right| = 13$ and $\left| \vec{a} \times \vec{b}\right| = 25$ find $\vec{a}\cdot\vec{b}$.

• A. $±10$
• B. $±40$
• C. $±60$
• D. $±25$

Answer 1

Answer: (C)

We know that
$\left| \vec{a} \times \vec{b}\right|^{2} + \left| \vec{a} \cdot \vec{b}\right|^{2} = \left|\vec{a}\right|^{2}\left|\vec{b}\right|^{2}$
$\Rightarrow \left(25\right)^{2}+\left| \vec{a} \cdot \vec{b}\right|^{2} = \left(5\right)^{2}\times\left(13\right)^{2}$
$\Rightarrow \vec{a} \cdot \vec{b} = \sqrt{3600}= \pm60$