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. $\pm 10$
• B. $\pm 40$
• C. $\pm 60$
• D. $\pm 25$

Answer 1

Answer: (C)

We know that
${\left|\vec{a}\times \vec{b}\right|}^2+{\left|\vec{a}\cdot \vec{b}\right|}^2={\left|\vec{a}\right|}^2{\left|\vec{b}\right|}^2$
$\Rightarrow {\left(25\right)}^2+{\left|\vec{a}\cdot \vec{b}\right|}^2={\left(5\right)}^2\times {\left(13\right)}^2$
$\Rightarrow \vec{a}\cdot \vec{b}=\sqrt{3600}=\pm 60$