Question

hi
why we use sin in vector product why not we use cosine?

Answer 1

that's the way it is defined...

Answer 2

the rule is AXB=lAllBlsin(theta)
where theta is the angle between the two vectors .
this is the definition of cross product it's unlike the dot product
the dot product
is just like the cross but replace the sine theta with cosine
A.B=lAl.lBlcos(theta)

Answer 3

your question is good but it's not sufficient to answer it in a single comment you need to read books and deeply understand the physical meaning of cross product to understand the issue

Answer 4

actually when we talk about cosine it is the projection of one vector on the other
like in this picture

Answer 5

further in vector product it is nothing like projections