Why is the addition/subtraction of vectors important?

Question

Why is the addition/subtraction of vectors important?

Answer 1

Being able to manipulate vectors is a very important skill for a student to master. Let me outline the physical motivation behind vectors.

In general, vectors are needed whenever we must mathematically describe a physical quantity orientated in space.

This situation occurs regularly in physics. (I would say it’s almost unavoidable)

Mechanics, electricity and magnetism are branches of physics where vectors are used often.

Specific examples are:
-forces acting on a box
-momentum of a rolling ball
-electric field from a positive charge

In each situation the physical quantity involved (force, momentum, electric field respectively) has magnitude (measurable size) and direction.

In other words, each physical quantity can be represented by a vector.

Thus, in physics, vectors are extremely important because they arise in many physical situations.

Answer 2

Well, here is a crushingly important situation in which vector addition/subtraction is crushingly important. You can express the gravitational force exerted on your body by the earth as a vector. Has magnitude and direction. ditto the Moon. different magnitude, and direction, both varying with time. ditto the Sun. similarly varying. ditto the Big Bus of Very Fat Women passing you on the street. Sum them all together and you will see why you are not standing up quite straight. And why the tide is out. And why it may be more likely or less likely for an earthquake to occur. There are lots of other applications, but not as much fun.

Answer 3

because when u have multiple vectors, u can combine them as one resultant. Using parallelogram law, uses adding and subtraction of vectors.

Answer 4

they are most important when we need to find the resultant of many more forces......!
then addition and subtraction of forces come into play....!