Area of parallelogram for 4 dimensional vector

Question

Hello, basically I just don't understand its explanation.

I also do not know what kind of formula it is used.. (It does look like it used some kinda formula)

Thank you very much if you can explain it well!!

Answer 1

This is the formula to use:

$||a||^2*||b||^2 - |a.b|^2$.

Which is the magnitude of a^2, magnitude of b^2 subtract the dot product of a.b^2.

Answer 2

Hint: Calculate the length of these two vectors and find the angle between them using inner product. After getting the height use the area formula.