Can all dot product computations be computed?

[camino]

Homework Statement

Which of the following can be computed?

1. A dot B dot C
2. A dot ( B dot C )
3. A dot ( B + C )
4. 3 dot A

Homework Equations

The Attempt at a Solution

I believe that 2 and 3 are the only two that can be computed. Can anyone confirm this? Thanks.

 

[Office_Shredder]

Why do you think that? What makes them different from the others?

I personally disagree with your answer

 

[camino]

Well I think 4 can't be computed because 3 is not a vector.

But perhaps 1 can be?

I'm almost certain 2 and 3 can be.

 

[Dick]

Well I think 4 can't be computed because 3 is not a vector.

But perhaps 1 can be?

I'm almost certain 2 and 3 can be.

The 3 isn't that much of a problem. 3 times something is ok for a lot of objects. But how do you compute dot(A)?? Imagine A, B and C are real vectors and try to figure out how you would compute any of these. Only one makes sense.

 

[Gregg]

I think the dot product is defined as being a scalar product between two vectors. For this reason I don't think any of the products except number 3 is acceptable:

A.B.C isn't compatible
A.(B.C) is A.(Scalar)
A.(B+C) = A.B + A.C both of which make perfect sense
3.A is not OK whilst 3A is.

 

[camino]

Thank you Gregg! Your explanation makes perfect sense to me and is exactly the help I was looking for!