Adding Vectors

A vector is a quantity which has both size and direction.
For example:
  • 25 km West
  • 180 Newtons up
  • 90 km/h right
  • 35 m at an angle of 17 degrees from horizontal
A vector can be represented by an arrow.
The length of the arrow shows the size of the vector.
The angle of the arrowshows the vector's direction.

This page is all about how to combine, or add, two vectors.

When two vectors are pointing in the same direction, the method for adding them is just a straight addition problem. For example, moving 20 km west, and then moving 15 km west, results in a total of 35 km west.

Similarly, if the two directions are pointing in exactly opposite directions, it's just a subtraction problem. For example, moving 20 km west, and then moving 15 km east, results in a total of 5 km west.

Here's a simple in-line vector addition problem in sports, relating to throwing a javelin.


It's when the two vectors are not pointing in the same or exactly opposite direction that adding them together gets a little complicated. For example, how would you find out the result of moving 20 km west, and then 15 km north? That's what this page is about.


Adding vectors: Vectors can be added several ways. 'Adding the vectors' means showing the sum vector, and finding its size and direction.



Finding the sum by:


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