Question

How do you find the cross product of vectors $?$

Answer 1

Finding the cross product of vectors:

The cross product of two vectors $\alpha$ and $\beta$ can be found using the formula

$\mathit{A}\mathbf{}\mathbf{\times }\mathbf{}\mathit{B}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\left|}\mathit{A}\mathbf{\right|}\mathbf{}\mathbf{\left|}\mathit{B}\mathbf{\right|}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{\left(}\mathit{\theta }\mathbf{\right)}\mathbf{}\mathit{n}$

Where

$\left|\alpha \right|$ is the magnitude of vector $\alpha$

$\left|\beta \right|$ is the magnitude of vector $\beta$

$\theta$ is the angle between vector $\alpha$ and $\beta$.

$n$ is the unit vector which is at the right angle to both the vectors.

Hence, we can find the cross product of vectors by the formula $\mathit{A}\mathbf{}\mathbf{\times }\mathbf{}\mathit{B}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\left|}\mathit{A}\mathbf{\right|}\mathbf{}\mathbf{\left|}\mathit{B}\mathbf{\right|}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{\left(}\mathit{\theta }\mathbf{\right)}\mathbf{}\mathit{n}$.