Vectors can be added in an obvious way. In the diagram below
goes from
to B and
goes from
to
The vector
goes fromtoWe can write
or
.Importantly,
so
If
is split in some ratio by some point
then we can find
using this ratio. Suppose
splitsin the ratio 2:3, then
is in the ratio 2/3 so that
and
We can label the triangle as below.
Then
For a slightly more complicated example, consider the parallelogram below, with
and
splitsin the ratio 1:2 andsplits
in the ratio 3:2. Find
Because ABCD is a parallelogram,
1.
so using the first ratio in the question
and
2.
so using the second ratio in the question
and
Then