is (u dot v)dot (a dot c) a scalar quantity or vector quantity?

Question

What's the difference?

(I'm thinking scalar since it has no direction and it only has magnitude.)

Answer 1

the dot product of 2 vectors is always a scalar. the difference between the two is that the scalar doesn't have direction, yes.

Answer 2

The dot product is an operation between any two vectors and is always a scalar, your

(u dot v)dot (a dot c)
= (a scalar) dot (a scalar)
which would be undefined, since there is no such thing as a dot product between two scalars.

Answer 3

What do you get when you cross a mosquito and a mountain climber?

Nothing. You cannot cross a vector and a scaler.