# Scalar 'dot' scalar = ?

#### u-will-neva-no

Joined Mar 22, 2011
230
Hey everyone, I have not been able to find an answer to this so maybe someone could help me out. I have the equation (A.B).(C.D) and I know that A.B and C.D result in a Scalar. This means that im trying to find the answer to a scalar 'dot' scalar.

Does this result in another scalar, vector or is this not possible? My instinct say it results in a scalar...Please let me know!!

#### steveb

Joined Jul 3, 2008
2,436
Hey everyone, I have not been able to find an answer to this so maybe someone could help me out. I have the equation (A.B).(C.D) and I know that A.B and C.D result in a Scalar. This means that im trying to find the answer to a scalar 'dot' scalar.

Does this result in another scalar, vector or is this not possible? My instinct say it results in a scalar...Please let me know!!
It's unusual to have all the dots look the same, but it seems that the dots inside the brackets are a dot product between vectors and the dot between the bracketed dot-products must be ordinary scalar multiplication between scalars. I imagine another interpretation might be possible, but that seems to be the sensible interpretation based on what you said.

#### u-will-neva-no

Joined Mar 22, 2011
230
So the actual dot between the two scalars, i.e. ().() (dont worry, im not trying to draw silly pictures) is actually a multiplication between the two? I thought that if I had something like (A.B)(C.D) then that was multiplication?

#### steveb

Joined Jul 3, 2008
2,436
So the actual dot between the two scalars, i.e. ().() (dont worry, im not trying to draw silly pictures) is actually a multiplication between the two? I thought that if I had something like (A.B)(C.D) then that was multiplication?
Yes, it is, but a dot can also be used for scalar multiplication. The unusual thing about your example is that usually people use two different looking symbol for dot product and scalar multiplication. They do this to avoid the confusion we are having now.

Often the dot product is a bold dot and the scalar multiplication is a tiny dot. Or it can by like in your example(A.B)(C.D).

Personally, I like to use a very fine dot for multiplication because it can avoid confusion. For example if you see f(t)g(x) you know it is the variable f as a function of t times the variable g which is a function of x. But someone might think you mean f times t times g times x. So, I like to write $$f(t) \cdot g(x)$$, which means ordinary multiplication between two scalar functions.

#### u-will-neva-no

Joined Mar 22, 2011
230
Oh I see. I think my example refers to the dot product between two scalars. After thinking about it, that would lead to the result of being a scalar. Say A.B=2 and C.D = 5 then my result would be 10 (a scalar). This makes sense to me but I could be wrong as usual...

#### steveb

Joined Jul 3, 2008
2,436
Oh I see. I think my example refers to the dot product between two scalars. After thinking about it, that would lead to the result of being a scalar. Say A.B=2 and C.D = 5 then my result would be 10 (a scalar). This makes sense to me but I could be wrong as usual...
All I can say is that what you are doing seems reasonable. Yes, we can both be wrong, but without any further information, that seems like the best guess.

#### u-will-neva-no

Joined Mar 22, 2011
230