Question

How do you find the cross product of an angle$?$

Answer 1

Finding cross product of an angle:

The angle $\theta$ between two vectors $A$ and $B$ can be found using the dot product and the cross product.

The angle between two vectors formulas given as:

Using dot product: $\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{-}\mathbf{1}}\mathbf{}\mathbf{\left(}\frac{\mathbf{A}\mathbf{}\mathbf{·}\mathbf{}\mathbf{B}}{\mathbf{\left|}\mathbf{A}\mathbf{\right|}\mathbf{}\mathbf{\left|}\mathbf{B}\mathbf{\right|}}\mathbf{\right)}\mathbf{}$

Using cross product: $\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{\mathbf{|}\mathbf{A}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{B}\mathbf{|}}{\mathbf{\left|}\mathbf{A}\mathbf{\right|}\mathbf{}\mathbf{\left|}\mathbf{B}\mathbf{\right|}}\mathbf{\right)}$

Hence, we can find the cross product of an angle by $\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{\mathbf{|}\mathbf{A}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{B}\mathbf{|}}{\mathbf{\left|}\mathbf{A}\mathbf{\right|}\mathbf{}\mathbf{\left|}\mathbf{B}\mathbf{\right|}}\mathbf{\right)}$