Why are VECTORS important

VECTOR, 1. A variable quantity that can be resolved into components. 2. A straight line segment whose length is magnitude and whose orientation in space is direction. (Princeton WordNet Database, as used in WordWeb Dictionary.)

Can you exemplify the difinition and make it more useful to me, thank you!

math goes on forever
we start by counting objects 1 = o , 2 = oo , 3= ooo etc
later we make pairs of numbers (..) but he (..) is itself one number of a different type, example a point on a graph

but Vector is an entirely different kind of "number" (, a, b) or (ai + bj ) depending on notation

then there are 3 or higher dimensional vectors and tensors and quadriaon, and complex numbers ...etc

the vectors are very useful in motion problems, complex numbers for AC electrical and higher math for modern physics.

Aircraft navigation. Where a crosswind will blow the plane off course over time. Knowing the vectors of the wind direction and velocity and the planes speed and direct, you can plot how much the plane will be blown off course.

Or in the case of a head wind. knowing that the wind is subtracting from your airspeed, how much faster you need to fly to arrive on time, how much fuel the plane will use and what the cost of that fuel will be.
http://www.raeng.org.uk/education/diplom…
http://www.whyslopes.com/5056Geometry_-_…