July 14th, 2018, 02:42 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 15th, 2018 at 12:39 AM. 
July 14th, 2018, 06:58 AM  #2  
Senior Member Joined: Feb 2010 Posts: 714 Thanks: 151  Quote:
$\displaystyle \vec{p} = \dfrac{\vec{b}+2\vec{c}}{3}$ 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 15th, 2018 at 12:40 AM.  
July 15th, 2018, 03:27 AM  #3 
Newbie Joined: Jul 2018 From: india Posts: 2 Thanks: 0 
Thank you


Tags 
geometry, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Two 3D Trigo Geometry Problems without using vector or coordinate geometry  whsvin  Geometry  0  February 1st, 2017 08:07 AM 
I think I found an error on my vector geometry test  mysteryoftheunknown  Geometry  3  April 16th, 2016 02:53 PM 
vector geometry question  danny88  Linear Algebra  3  May 11th, 2014 01:40 PM 
vector geometry  Proff  Geometry  3  October 9th, 2013 12:21 AM 
geometry + vector  mikeportnoy  Geometry  5  November 10th, 2009 11:32 PM 