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In this section, we shall learn the basics of vectors ...
What are vectors?
A vector is an entity which has magnitude and direction. Magnitude is another word for length (or size), so a vector has size and direction. Moreover (and a point that is perhaps often understated), it is the size and direction combination possessed by a vector that sets it apart from (or equates it to) another vector. So, two vectors that have the same size and direction are equal, but if there are any differences in either magnitude or direction (or both), then they are not equal.
The best way of illustration, as with most things, is by example.
Imagine two flying aircraft, each with their own target destination. Suppose both are flying at 300 mph – then their speeds are equal. All that would be important to a passenger wanting to know how long their flight will take is how far they are travelling and the speed of the plane. To the air traffic controller (ATC), however, three properties of each aircraft are important: where each is, what speed each is flying at, and the direction each is flying in. With this information, the ATC can determine whether or not there will be a collision.
For each aircraft, the speed and direction of flight are properties of the plane’s motion and, combined, they define its velocity. The position of the aircraft, though also of vital importance to the ATC, isn’t a property of the motion of the plane. In this example, the vector is the velocity, the magnitude is the speed and the direction is the flying direction.
If both planes in our example are flying at 300 mph and parallel to each other,
then they share the same velocity. In this case, they can never possibly collide
(assuming, of course, they start off apart). If you were sitting in one plane
and looking at the other one, it would appear to be stationary
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