Science, Maths & Technology

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# 3.3 Vector subtraction in component form

When subtracting a vector visually it is first necessary to find the negative of the vector being subtracted by reversing its direction. Algebraically, a similar process is followed, but if we follow the standard rules of algebra, it is a much more intuitive process. For example, consider the vector expression where the vector is subtracted from the vector . We can make sense of this by writing the expression as

where is the negative of . The negative of a vector has the same magnitude but the opposite direction, and for a vector we say its negative is

With this in mind, we can say that to subtract vectors in component form, we subtract each component of one vector from the corresponding component of the other.

## Subtracting vectors in component form

If and , then

In column notation, if and , then

## Example 4 Calculating vector subtraction in component form

Let and . Find .

### Solution

Subtracting the components of from the corresponding components of  gives

## Activity 16

Find the following vectors.

• a.

• b.

• c.