Learning vectors: the dot product of vectors

[singleton]

Well, I've been attempting to learn dot products of vectors and in doing so have come upon some questions.

NOTE:
a, b, and c are to be regarded as vectors
Please regard '*' as the dot for multiplication, too.

Question 1:
a * b * c

When I see this, I am unaware how to approach it. Should I tackle it left to right as I would normally?

a * b will yield a scalar value using the dot product. Then if I take the result and * c, I will have a scalar multiple times a vector. So the result is a vector?

OR do I do a1*b1*c1 + a2*b2*c2 + a3*b3*c3 and the result is a scalar?


Question 2:
(a * b) * c
I would naturally attack the brackets first of all and the resulting value will be scalar. Then continuing on, I have a scalar result value times the vector c. So, the final result is a scalar multiple of vector c, correct?

 

[matt grime]

a.b.c makes no sense (a.b)c does as does a(b.c) and they are different. where does thsi come from? i mean who is using the same symbol for dot product (defined only on two vectors in the same vector space) and scalar mult?

 

[singleton]

They are from questions in the book I'm attempting to learn from.

So, the dot product symbol cannot be used to express multiplication between scalar and a vector?

(I am unaware, I had always thought the dot was general multiplication, interchangable with the "x" symbol).

The book asks you to categorize the results of the expressions.

One of the categories is undefined, so that is where a.b.c would end up.

 

[matt grime]

yes the book is attempting to make you realize tht you can only form the dot product between two vectors (in the same space, so you can't dot a vector in R^2 with one in R^3)

 

[Yegor]

Once i saw a*b*c [or (a,b,c)], and it was supposed to be mixed multiplication $$(\vec{a}\times\vec{b})*\vec{c}$$ (or $$(\vec{a}*(\vec{b}\times\vec{c})$$, no difference) By x i mean vectorial multiplication.

 

[singleton]

Thanks. This cleared up the problems I was having :)

I had encountered the dot before and wrongly assumed that it meant general multiplication, just another symbol. I was wrong ;)

Unfortunately the book didn't give to much on the use of the symbol. It just introduced it as "here, this is the algebraic formula for dot products and this is the geometric formula". Then it asked me those questions. So I was confused to say the least...

thanks again!