Take the examples of all directed arrows (every possible length and every possuangle) originating from a single point.

Now in this set vector addition is like addition of forces in physics: parallelogram law. In this set internally there is addition. Also there is an external operation. Any vector can be "scaled up/down" by any real number. This real number is not part of the set of arrows. But it makes sense to talk of 3.75 times a force. SImply a force directed in the same way but with with strength 3.75 times the original. This is depcied as an arrow of that length in the same direction.

In general any set where we can add them among themselves, and multiply by an external scalar usually the set of real numbers subject to some expected conditions is called a vector space.

Take the examples of all directed arrows (every possible length and every possible angle) originating from a single point.

Now in this set vector addition is like addition of forces in physics: parallelogram law. In this set internally there is addition. Also there is an external operation. Any vector can be "scaled up/down" by any real number. This real number is not part of the set of arrows. But it makes sense to talk of 3.75 times a force. SImply a force directed in the same way but with with strength 3.75 times the original. This is depicted as an arrow of that length in the same direction.

In general any set where we can add them among themselves, and multiply by an external scalar usually the set of real numbers subject to some expected conditions is called a vector space.