Expert: Paul Soderman - 12/5/2009

Question
why we use the systematic form of what called the vectors as we can solve the problems easily without vectors ie why we say v=omega(as vector)cross the position vector and try to solve the determined or the array to get the answer of the linear velocity ,,, we can say v=w*r*sin(x)
**i am a student in aerospace department faculty of eng. cairo university

Answer
Why do we use vectors...  Vectors are a very convenient way to describe a field such as a velocity field in a fluid.  Velocities have magnitude and direction - hence vectors are used extensively in fluid mechanics and many other branches of physics.  Once we have vectors, we can then manipulate them to get solutions to problems.  I believe you are studying cross products.  Vector cross products come in handy for solving certain types of problems. There may be other ways to solve the problems, but cross products are often simple and elegant.  For example, if the vector n is parallel to line L and r is a position vector with endpoint on L.  The the cross product n x r = d is an equation of L.  Cross products are just one more tool in our toolbox.
Paul