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 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:
Activity 17
Find each of the following vectors in component form.
a., where , and
b.
c., where and are any scalars