
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 7th, 2019, 03:05 AM  #1 
Senior Member Joined: Jun 2017 From: Lima, Peru Posts: 108 Thanks: 2 Math Focus: Calculus  How can I find the resultant and norm from pair of vectors passing in half a circle?
I've been walking in circles (no pun intended) with this problem. It states as follows: A certain sugar is analyzed at an optical laboratory. The tecnician passes two beams in the visible spectra one orange and the other lightblue. These describe the vectors labeled A and B (see the figure from below). Find the modulus of the resultant vector if it is known the radius is 2 micrometers. The alternatives given on my book are: $\begin{array}{ll} 1.&2\,\mu m\\ 2.&6\,\mu m\\ 3.&2\sqrt 3\,\mu m\\ 4.&4\, \mu m\\ 5.&\sqrt 3\, \mu m\\ \end{array}$ Typically I would try to show some attempt to solve this problem but here I'm stuck at the very beginning. I tried all sorts of manipulations with the vectors. But I couldn't really reach to a logical arrangement to obtain a resultant. In other words I got tangled with too many arrows. Can somebody help me with this?. If possible I'd appreciate a graphical and simple approach with less algebraic manipulations if possible. Please try to accompany the explanation with some sort of drawing so I can see what's happening because I feel this kind of question does really need that, otherwise I'll not be able to "understand" what's going on. 
October 7th, 2019, 07:48 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,035 Thanks: 2271  Semihex.PNG In the above diagram, I've constructed some equilateral triangles whose sides are of the same length as the radius of the circle. Note that the lines GC and AG correspond to your vectors. Hence, you are effectively asked for the length of AC, which you can see is twice the length of an altitude of one of the equilateral triangles, so it's easily calculated to be 2√3 μm. You will first need to find a few angles, so that you can show that my diagram is valid. You might choose to add other lines to the diagram or omit the line CD. 

Tags 
circle, find, half, norm, pair, passing, resultant, vectors 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
3 vectors and the resultant vector  MathsLearner123  Geometry  1  June 10th, 2019 09:02 AM 
Circumference of smaller half circle removed inside of half circle?  DecoratorFawn82  Algebra  3  September 14th, 2018 08:59 AM 
Vectors and Norm  dave22  Calculus  3  November 3rd, 2016 11:45 AM 
How can I know that vector x is passing b/w vectors a, b, c, d?  bilal auib  Algebra  2  June 23rd, 2014 10:49 AM 
Find The Standard Equation Of The Circle Passing...  soulrain  Algebra  7  January 9th, 2012 07:44 PM 