In Chapter 1 we found that 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.
If and
, then
In column notation, if and
, then
Let and
. Find
.
Subtracting the components of from the corresponding components of
gives
Find the following vectors.
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