Part 2: Chapter 4 Applications of vectors

# 4.3.4 Combining vector operations

When using vectors to model engineering systems it is often necessary to carry out multiple operations to combine vectors in different ways. When vectors are expressed in component form, combining operations involves following the standard rules of algebra. In the next example, the vector operations of addition, subtraction and scalar multiplication are combined.

## Example 4.5 Simplifying a combination of vectors in component form

Let , and .

Find in component form.

#### Solution

Substitute in the expressions for , and in terms of and , and then simplify:

Note: A tutorial clip of this example is provided on the module website.

## Activity 4.17

Find each of the following vectors in component form.

1. , where , and

3. , where and are any scalars

OpenLearn - Part 2: Chapter 4 Applications of vectors
Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.