Hi,I've been looking at vector mechanics applied to physical problems and I am stuck on one aspect which is upsetting me as it means I don't have a full understanding.
My problem is in calculating scalar products. Given 3 vector planes I,j and K , I do not understand why i.I=1, j.j=1,k.k=1 and j.k=0,i.j=0 and k.I=0 .
Especially the last 3 . Why do they equal zero? What should I be visualising in order to understand this?
I could see straight away what these products are when I was learning vector products as I could visualise the vector product vector at right angles to the plane of any 2 but am getting nowhere with scalar products :(
Please help.

Fred

okay, i, j and k are the unit vectors in each of the 3 directions i.e. they have length 1.

Basically the dot product is the magnitude of the vector when it is projected onto another vector.

since i, j and k are all perpendicular, their dot product is 0, that is they have 0 magnitude in the direction of the other vectors.

the dot product of a unit vector with itself is 1, because it has magnitude 1 in its own direction.

Here is what you should be visualising:

This is A.B = |A|cos\theta, in your cases \theta is either 0 or 90.

http://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Scalarproduct.gif/300px-Scalarproduct.gif