April 26th, 2017, 02:15 AM  #1 
Newbie Joined: Apr 2017 From: UK Posts: 1 Thanks: 0  Little Vectors questions
Hi Can someone help me with this question. Vectors p q and r are such that p. (q+r) = q . (p+r) Show that r must be perpendicular to pq Thanks in advance if anyone can help!! 
April 26th, 2017, 04:07 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,709 Thanks: 458 
$p \cdot (q + r) = q \cdot (p + r)$ $\implies p \cdot q + p \cdot r = q \cdot p + q \cdot r$ (by bilinearity). Now if we are in a real vector space, which I suppose is assumed here, we have $p \cdot q = q \cdot p$. Note that in a complex vector space this does not hold, rather we have $p \cdot q = \overline{q \cdot p}$, the complex conjugate. Just mentioning this because commutativity of the dot product can not always be assumed. However in this case we'll assume our vector space is over the real numbers so that we have $p \cdot r = q \cdot r \implies (p  q) \cdot r$ (by the bilinearity of the dot product) which shows that $p  q$ and $r$ are orthogonal. Last edited by Maschke; April 26th, 2017 at 04:10 PM. 
April 26th, 2017, 05:15 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,709 Thanks: 458 
Typo  Last implication is supposed to be $p \cdot r = q \cdot r \implies (p  q) \cdot r = 0$. 

Tags 
questions, vectors 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Can anyone help me solve these questions? modulo questions  vickyc95  Number Theory  4  May 24th, 2016 08:20 PM 
Hard questions on vectors?  neelmodi  PreCalculus  1  September 6th, 2014 06:42 PM 
vectors  arron1990  Linear Algebra  0  February 24th, 2012 01:51 AM 
Maths questions on dot product, vectors?  latkan  Linear Algebra  1  May 14th, 2009 09:39 AM 
Vectors.  Lisa  Linear Algebra  0  November 16th, 2008 12:14 AM 