The Cross Product of two unit vectors has length $1$: True/False?

Question

Shouldn't equal one always because cross product result is not equal to one all the time yeah?

Started with two random unit vector magnitudes.

Let's say: $a=\left(\frac{1}{2}, \frac{1}{2}\right)$, $b=\left(\frac{1}{\sqrt{8}}, \frac{1}{\sqrt{8}}\right)$, $|a|=\frac{1}{2}$, $|b|=\frac{1}{4}$

Then I cram into cross product $|a||b|\sin(\theta)= \left|\frac{1}{2}\right|\left|\frac{1}{4}\right|\sin(\arcsin(\theta))$.

Answer 1

Clearly this cannot be true, since the cross product of two parallel unit vectors will always be the $0$ vector. That said, the vectors you chose are not unit vectors. Unit vectors have magnitude 1.