Vector addition using components

Vector addition using components

In the previous section we have learnt about addition and subtraction of two vectors using geometric methods. But once we choose a coordinate system, the addition and subtraction of vectors becomes much easier to perform.

The two vectors  and  in a Cartesian coordinate system can be expressed as

Then the addition of two vectors is equivalent to adding their corresponding x, y and z components.

Similarly the subtraction of two vectors is equivalent to subtracting the corresponding x, y and z components.

The above rules form an analytical way of adding and subtracting two vectors.