How to visualize right hand side of the equation $\pmb a\times \pmb b= |\pmb a||\pmb b|\sin \theta \ \hat{\pmb n}$

Question

I know how to visualize cross product but what is the proof and how to visualize right hand side of the following equation

$$\pmb a\times \pmb b= |\pmb a||\pmb b|\sin \theta \ \hat{\pmb n}$$

Answer 1

As for visualization, then the absolute value of right hand side is the area of parallelogram with sides $a$ and $b$. Picture, for example, is here sharetechnote.com

Answer 2

Here is a visual for the right-hand-side of $$\pmb a\times \pmb b= ab\sin \theta \ \hat{\pmb n}$$

1) The unit vector n is perpendicular to both a and b

2) The scalar $ab\sin\theta$ is just the area of the parallelogram formed by a and b.