Posted by vectors? on Sunday, January 23, 2011 at 10:06pm.
A vector has both magnitude and direction. A good example is the difference between speed and velocity.
You can measure speed with just a speedometer, but for velocity you need both the speedometer and a compass.
When you add vectors you must take account of both their speeds and directions.
One way is graphically using the sum as the diagonal of a parallelogram with the sides being the two vectors.
Another way which is much more suited to computation is to find the components of both vectors in somme perpendicular axis system containing the vecors. That works because perpendicular vectors are "othogonal", changing a component in one of the axis directions does not affect the component on the other axis.
Then components of the to vectors may be added on each axis and a resultant found from the results.
In such a system the component of a vector along an axis is the magnitude of the vector times the cosine of the angle between vector and axis.