 My Math Forum How can I find the resultant and norm from pair of vectors passing in half a circle?
 User Name Remember Me? Password

 Geometry Geometry Math Forum

 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. Thanks from idontknow 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MathsLearner123 Geometry 1 June 10th, 2019 09:02 AM DecoratorFawn82 Algebra 3 September 14th, 2018 08:59 AM dave22 Calculus 3 November 3rd, 2016 11:45 AM bilal auib Algebra 2 June 23rd, 2014 10:49 AM soulrain Algebra 7 January 9th, 2012 07:44 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      