Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Task: In parallelogram OABC sides AB and BC have the centers D and E. Prove with vectors that vectors OD and OE divide the Diagonal vector AC into three equal parts.

I got this task from my teacher and i couldn't do it and i'd just like to see how it is supposed to be done just for my interest.

share|cite|improve this question
up vote 0 down vote accepted

Have you seen any other problems in which you have to find out where two vectors intersect?

Rather than showing you the solution, here are some steps to try.

In two dimensions you need two basis vectors - I'd suggest using OA and OB and writing everything in terms of those.

Then name the point at which OD meets AC - say F.

Then put OF = xOD and AF = yAC. Written in terms of basis vectors you get two equations in the two unknowns x and y, which you should be able to solve.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.