Thread: vectors

and represent the sides of PQ and PR of a triangle PQR respectively . If S is the midpoint of QR , show that the

I managed to prove this .

Using the method above or otherwise , find the position of O which is located in the triangle PQR where

need help on this part.

Hello hooke

Originally Posted by hooke

and represent the sides of PQ and PR of a triangle PQR respectively . If S is the midpoint of QR , show that the

I managed to prove this .

Using the method above or otherwise , find the position of O which is located in the triangle PQR where

need help on this part.

Here's a hint.

You've just shown that . Now find and in the same way, where are the mid-points of and respectively.

Then add and together.

What happens next?

Grandad

Originally Posted by Grandad

Hello hookeHere's a hint.

You've just shown that . Now find and in the same way, where are the mid-points of and respectively.

Then add and together.

What happens next?

Grandad

thanks , yeah , i got 0 . It looks to me O is the centroid of the triangle but i am not sure how to describe the position of O .

Hello hooke

Originally Posted by hooke

thanks , yeah , i got 0 . It looks to me O is the centroid of the triangle but i am not sure how to describe the position of O .

Just say it's the centroid - that would be good enough for me!

Grandad

Originally Posted by Grandad

Hello hookeJust say it's the centroid - that would be good enough for me!

Grandad

thanks , but the book says O divides PS into a ratio of 2:1 , i am not sure how to get that .

Hello hooke

Originally Posted by hooke

thanks , but the book says O divides PS into a ratio of 2:1 , i am not sure how to get that .

It is a well-known fact that the centroid divides each of the medians in the ratio 2:1. For a vector proof, see here.

Grandad