Question

Can you cross product a scalar and a vector?

Answer 1

Cross product :

A cross product can be applied only on two vectors, it cannot be applied to a scalar and a vector.

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

where, $\left|A\right|=$Length of vector $A$

$\left|B\right|=$Length of vector $B$

$\theta =$Angle between $A$ and $B$

$\hat{n}=$Unit vector perpendicular to the plane containing $A$ and $B$

$\therefore A$ and $B$ cannot be a scalar

Hence, we cannot cross product a scalar and a vector.