My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 14th, 2018, 01:42 AM   #1
Newbie
 
Joined: Jul 2018
From: india

Posts: 2
Thanks: 0

vector geometry

ABC is a triangle, P divides BC in the ratio 2:1, and Q divides AC in the same ratio. AP and BQ meet at X. Find in what ratio AP and BQ are divided by X? (Prove by vector method.)

Last edited by skipjack; July 14th, 2018 at 11:39 PM.
chandan gowda is offline  
 
July 14th, 2018, 05:58 AM   #2
Senior Member
 
mrtwhs's Avatar
 
Joined: Feb 2010

Posts: 683
Thanks: 129

Quote:
Originally Posted by chandan gowda View Post
ABC is a triangle, P divides BC in the ratio 2:1, and Q divides AC in the same ratio. AP and BQ meet at X. Find in what ratio AP and BQ are divided by X? (Prove by vector method.)
Assuming you mean $\displaystyle \dfrac{BP}{PC}=\dfrac{2}{1}$ and $\displaystyle \dfrac{AQ}{QC}=\dfrac{2}{1}$ and assuming that $\displaystyle \vec{a}$ is the vector from an arbitrary origin to the point $\displaystyle A$, we can say the following:

$\displaystyle \vec{p} = \dfrac{\vec{b}+2\vec{c}}{3}$ and $\displaystyle \vec{q} = \dfrac{\vec{a}+2\vec{c}}{3}$.

So, $\displaystyle 3\vec{p} = \vec{b}+2\vec{c}$ and $\displaystyle 3\vec{q} = \vec{a}+2\vec{c}$.

Subtracting we get $\displaystyle 3\vec{p}-3\vec{q}=\vec{b}-\vec{a}$ or $\displaystyle 3\vec{p}+\vec{a}=3\vec{q}+\vec{b}$

and $\displaystyle \dfrac{3\vec{p}+\vec{a}}{4}=\dfrac{3\vec{q}+\vec{b }}{4}=\vec{x}$.

So $\displaystyle X$ divides each cevian into a ratio of $\displaystyle 3:1$.

Last edited by skipjack; July 14th, 2018 at 11:40 PM.
mrtwhs is offline  
July 15th, 2018, 02:27 AM   #3
Newbie
 
Joined: Jul 2018
From: india

Posts: 2
Thanks: 0

Thank you
chandan gowda is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
geometry, vector



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Two 3-D Trigo Geometry Problems without using vector or coordinate geometry whsvin Geometry 0 February 1st, 2017 07:07 AM
I think I found an error on my vector geometry test mysteryoftheunknown Geometry 3 April 16th, 2016 01:53 PM
vector geometry question danny88 Linear Algebra 3 May 11th, 2014 12:40 PM
vector geometry Proff Geometry 3 October 8th, 2013 11:21 PM
geometry + vector mikeportnoy Geometry 5 November 10th, 2009 10:32 PM





Copyright © 2018 My Math Forum. All rights reserved.