I was reading this document :
http://math.kennesaw.edu/~plaval/math4490/rotgen.pdf


Here the author says that from this figure
http://i.stack.imgur.com/KBw9l.png


that we can express $v_{\perp}$ like this :



I don't understand this part. Can anybody explain how is ?

The first term: should be evident from the figure. The second term is a bit trickier to understand - the w vector has magnitude equal to , but is at 90 degrees to it. So the magnitude of the term is equal to the magnitude of, but points in the w direction. The vector w in turn is defined by . Hope this helps.

Hello, Thanks for the answer. I understood that part. But thing i did not understood is that how can we express as addition of , that is the addition of its 2 component and . Is it same as meaning of 2 vector addition like Vab = Va + Vb?