is (u dot v)dot (a dot c) a scalar quantity or vector quantity?
What's the difference?
(I'm thinking scalar since it has no direction and it only has magnitude.)
the dot product of 2 vectors is always a scalar. the difference between the two is that the scalar doesn't have direction, yes.
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.
What do you get when you cross a mosquito and a mountain climber?
Nothing. You cannot cross a vector and a scaler.
To determine whether (u dot v)dot (a dot c) is a scalar quantity or a vector quantity, let's break down the different terms and understand their properties.
First, let's consider the dot product of two vectors, u and v. The dot product of two vectors results in a scalar quantity. It's calculated by multiplying the corresponding components of the vectors and then summing them up. The dot product only considers the magnitudes of the vectors and does not take into account their directions. Therefore, (u dot v) is a scalar quantity.
Next, let's consider the dot product of two other vectors, a and c. Similar to the previous case, the dot product of a and c also results in a scalar quantity. Again, it only considers the magnitudes of the vectors.
Now, when we take the dot product of these two resulting scalar quantities, (u dot v) and (a dot c), the overall result is a scalar quantity. This is because scalar quantities can be multiplied together, and the result will still be a scalar.
So, to answer your question, (u dot v)dot (a dot c) is indeed a scalar quantity. Your intuition is correct that scalar quantities have magnitude but no direction. They represent quantities like temperature, mass, time, and energy. In contrast, vector quantities have both magnitude and direction and are used to represent physical quantities like displacement, velocity, force, and acceleration.