Vector Division Question

## Question:

can you tell me how do you divide vectors( definition, diagrams & examples).

I would be very thankful if tell me how:

## Answer:

Division may be thought of as unmultiplying...you know, find the number which when multiplied by 3 yields 6. In this example the answer is obviously 2. In vectors there are two ways of multiplying, the dot product and the cross product. Vector division then should either undot a vector and a scalar or uncross a pair of vectors.
The difficulty is that there are more than one vector that when dotted with (a,b) yields 6, for example. We know this because the dot product of (a,b)·(c,d) is ac+bd=6. If we know a and b there are still two unknowns in the equation ac+bd=6. Any pair if numbers which satisfy this equation would qualify as the quotient of 6·/(a,b). Therefore dot division is not defined. Likewise there are infinitely many vectors which when crossed with (a,b,c) give us (d,e,f). Consider that AXB=C=|A||B|sin(q), where q is the angle from A to B. Any vector V in the plane of A and B where |V|sin(u)=|B|sin(q) will yield the same cross product. Again there are two unknowns, |V| and u, in the equation so there are infinitely many answers. Therefore cross division is also undefined.