May 3rd, 2018, 05:22 AM  #1 
Newbie Joined: Aug 2017 From: Norway Posts: 10 Thanks: 0  Length of vectors
Hey! I need some help with this task: Suppose that u1,u2 is an orthonormal basis of R2, that means u1*u2=0 and ui*ui=1, i=1,2. Let y=[<y1,y2>] be a vector in R2 and v = y1u1 + y2u2. Show that the vectors y and v are equal in length. The v vector is a sum of two scalar products. I don't see how I can calculate the length directly. Thanks 
May 3rd, 2018, 08:28 AM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,312 Thanks: 1224  Quote:
$y_1,~y_2$ are elements of a vector, not vectors themselves. In this case the easiest route is probably $\begin {align*} &\v\ = \sqrt{v\cdot v} = \\ \\ &\sqrt{(y_1 u_1 + y_2 u_2)\cdot (y_1 u_1 + y_2 u_2)} = \\ \\ &\sqrt{2y_1 y_2 u_1 \cdot u_2 + y_1^2 u_1\cdot u_1 + y_2^2 u_2 \cdot u_2} = \\ \\ &\sqrt{0 + y_1^2 + y_2^2} = \\ \\ &\sqrt{y_1^2 + y_2^2} = \\ \\ &\y\ \end{align*}$  

Tags 
length, vectors 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Arc Length given Chord Length & Height  mms  Math  10  July 31st, 2015 08:11 AM 
Arc Length  joshbeldon  Calculus  3  February 26th, 2015 12:58 PM 
Calculate distance between two limited length vectors  iqbad  Algebra  1  April 12th, 2013 04:38 PM 
arc length  summychan  Calculus  14  October 8th, 2012 09:15 PM 
find length if angle and length is given...  amin7905  Algebra  4  July 19th, 2012 02:08 PM 