How to find a unit vector normal to a plane containing Vectors A & B

Question

Vectors A and B are given. The solution provided by the professor says this is the answer:
$\frac{\vec{A}*\vec{B}}{|\vec{A}||\vec{B}|}$
I did a bit of Googling and various website says this is the correct way to find the unit vector normal to a plane:
$\frac{\vec{A}*\vec{B}}{|\vec{A}X\vec{B}|}$
Which one is correct?

Answer 1

Guide:

• substitute in some vectors and you can figure out which one is wrong isn't it.

• Note that for $u \ne 0$, $\|\frac{u}{\|u\|}\|=1$

• Note that for cross product, $\|u \times v\| =\|u\|\|v\|\sin \theta $

Answer 2

By cross product, it is equal to

$$\vec n=\frac{\vec{A}\times\vec{B}}{|\vec{A}||\vec{B}|\sin \theta}$$