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.
Let ,
and
.
Find in component form.
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.
Find each of the following vectors in component form.
, where
,
and
, where
and
are any scalars
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