# Math Help - Vectors cross product

1. ## Vectors cross product

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are vectors then show that

$\left | \mathbf{b} \times \mathbf{c} \right | \left | \mathbf{a} \right | \left | \cos\left(\theta\right) \right | = \left | \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) \right |$

Where $\theta$ is the angle between $(\mathbf{b} \times \mathbf{c})$ and $\mathbf{a}$

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are not coplanar.

2. Originally Posted by usagi_killer
If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are vectors then show that

$\left | \mathbf{b} \times \mathbf{c} \right | \left | \mathbf{a} \right | \left | \cos\left(\theta\right) \right | = \left | \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) \right |$

Where $\theta$ is the angle between $(\mathbf{b} \times \mathbf{c})$ and $\mathbf{a}$

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are not coplanar.
$\mathbf{a}\cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos{\theta}$.

Replace $\mathbf{b}$ with $\mathbf{b}\times \mathbf{c}$.