## Vectors 2

Vectors can be added in an obvious way. In the diagram belowgoes fromto B and goes fromto

The vectorgoes fromtoWe can writeor .Importantly,so

Ifis split in some ratio by some pointthen we can findusing this ratio. Supposesplitsin the ratio 2:3, thenis in the ratio 2/3 so that andWe can label the triangle as below.

Then

For a slightly more complicated example, consider the parallelogram below, withandsplitsin the ratio 1:2 andsplitsin the ratio 3:2. Find

Because ABCD is a parallelogram,

1.so using the first ratio in the questionand

2.so using the second ratio in the questionand

Then