My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

Thanks Tree1Thanks
  • 1 Post By Chemist116
LinkBack Thread Tools Display Modes
October 7th, 2019, 03:05 AM   #1
Senior Member
Chemist116's Avatar
Joined: Jun 2017
From: Lima, Peru

Posts: 108
Thanks: 2

Math Focus: Calculus
Question 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:

1.&2\,\mu m\\
2.&6\,\mu m\\
3.&2\sqrt 3\,\mu m\\
4.&4\, \mu m\\
5.&\sqrt 3\, \mu m\\

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
Chemist116 is offline  
October 7th, 2019, 07:48 AM   #2
Global Moderator
Joined: Dec 2006

Posts: 21,035
Thanks: 2271

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.
skipjack is offline  

  My Math Forum > High School Math Forum > Geometry

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

Copyright © 2019 My Math Forum. All rights reserved.