Vectors have a lot of applications in physics and engineering. Velocity, acceleration and forces are vectors.
For example, you can use vectors to determine the total distance travelled by a boat travelling across a river at 25 miles/hour while the river flows perpendicular to the boat at 10 miles/hour.
There are loads of other applications. Vectors can be used to predict the movement of planets in their orbits, and are useful for 3D geometry in general. Vectors are also essential in electromagnetics, where they are used to represent electric and magnetic fields and their relationships. Maxwell's equations are equations which use vectors. The Poynting vector is used to calculate the flow of electromagnetic energy through space, for example by radio waves or light.
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Vectors are used whenever there is a measurement in which not only the magnitude is relevant, but also the direction. Typical uses of vectors include position, velocity, acceleration, force, torque, and others.
Vectors are used to denote or model directions.
The law is used to add vectors to find the resultant of two or more vectors acting at a point.
Cloning vectors are used to increase the number of copies of the cloned gene or to amplify a foreign gene. Expression vectors are used to increase the expression of the foreign gene product.
In signals eigen values and eigen vectors are used in finding directions.... Signals are based on eigen vectors