Expert: James Gort - 5/7/2007

Question
Hi,I've been looking at vector mechanics applied to phycical problems and I am stuck on one aspect which is upsetting me as it means I dont 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 theese 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  

Answer
Hi Fred,

Scalar products are actually easier to understand than cross products.  The definition of a scalar (dot) product is A.B = AB cos (theta).  In the case of unit vectors j and k, these are at 90 degrees, so the cosine is zero.  Hope that helps!

Prof. James Gort