Thread: Vector triangle problem...

1. Vector triangle problem...

ABC is a triangle. D is the mid-point of BC, E is the mid-point of AC, F is the mid-point of AB and G is the mid-point of EF. Express the displacement vectors AD and AG in terms of OA, OB, and OC.

I am totally lost with this one. I have tried several drawings but I guess all of them were wrong. Please help!

2. Here are two strong hints.
$\overrightarrow {AB} = \overrightarrow {OB} - \overrightarrow {OA} \,\& \,\overrightarrow {AD} = \overrightarrow {AB} + \frac{1}
{2}\overrightarrow {BC}$

3. Thanks.. But I cannot understand how did that happen. I have been studying vectors for several hours but I don't get it.

I guess that was from the parallelogram law of vectors? I do understand how can AB be OB - OA but I do not understand how's the AD derived.

Do you have a link that explains the same concept?

4. ${\color{red}\overrightarrow {AD}} = \overrightarrow {AB} + {\color{blue} \frac{1}{2}\overrightarrow {BC}}$