what does the value of the dot product of two vectors tell us?

Question

what does the value of the dot product of two vectors tell us?

In: 10

Answer 1

Depends what the vectors are.

If your vectors are force and motion, the dot product tells us the total work done. If your vectors are the electric field gradient and charge flux, it tells us the power per unit length.

Usually, dot products arise when multiplication happens but in multi-dimensional space where the things being multiplied may not be in the same direction. This actually also applies to cross products, though, so don’t treat this as an exhaustive definition or anything.