My Math Forum Is there a way to obtain the modulus of desired sum from these vectors?

 Geometry Geometry Math Forum

 October 13th, 2019, 04:08 AM #1 Senior Member     Joined: Jun 2017 From: Lima, Peru Posts: 188 Thanks: 5 Math Focus: Calculus Is there a way to obtain the modulus of desired sum from these vectors? The problem is as follows: Find the modulus of the resultant vector which are seen in the quadrilateral shown below. Consider M and N to be mid points and \overline{MN}=20 The alternatives given on my book are: $\begin{array}{ll} 1.&20\\ 2.&40\\ 3.&60\\ 4.&80\\ 5.&50\\ \end{array}$ I'm stuck at this problem. First off, I'm not sure whether the schematic is incomplete (I've copied it down from my book). The reason for what I believe that seems incomplete is that I don't why $\overline{MN}=20$ is not in the picture. Will it affect the answer? I don't know what was intended by the one who posed this question. I really need guidance with this question as I don't know how on earth I could manipulate the existing vectors to obtain a logical sum. Can somebody help me with this using geometry or something trig-free?. As I mentioned, this problem seems kind of incomplete and I believe a drawing or some sketch which could accompany the answer would be much better to aid my understanding. Last edited by skipjack; October 13th, 2019 at 07:06 AM.
 October 13th, 2019, 07:02 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,124 Thanks: 2332 Let the lower dashed line be ANB. As $\vec{u} + \vec{v} = \vec{MA} + \vec{MB}$ (I hope you can see why), the modulus of $\vec{u} + \vec{v}$ is twice the length of MN. Thanks from idontknow
October 15th, 2019, 10:15 PM   #3
Senior Member

Joined: Jun 2017
From: Lima, Peru

Posts: 188
Thanks: 5

Math Focus: Calculus

Quote:
 Originally Posted by skipjack Let the lower dashed line be ANB. As $\vec{u} + \vec{v} = \vec{MA} + \vec{MB}$ (I hope you can see why), the modulus of $\vec{u} + \vec{v}$ is twice the length of MN.
As I mentioned above, my first impression was that this problem was incomplete. But it doesn't seem that. Can you add some drawing to aid me understand the justification for this answer? I don't know exactly how to get to that equality that you had shown; if you could draw the arrows over my drawing or make one, I could understand. Can you help me with that?

Last edited by skipjack; October 16th, 2019 at 09:30 AM.

 October 16th, 2019, 09:35 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,124 Thanks: 2332 VectorSum.PNG As M is the midpoint of CD, $\vec{MC} = -\vec{MD}$. $\vec{MA} + \vec{MB} = \vec{MD} + \vec{u} + \vec{MC} + \vec{v} = \vec{u} + \vec{v}$ As MN is the relevant median of triangle MAB, $\vec{MA} + \vec{MB} = 2\vec{MN}$.

 Tags desired, modulus, obtain, sum, vectors

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post raul21 Elementary Math 13 August 27th, 2017 05:59 PM honzik Abstract Algebra 0 January 4th, 2011 12:36 PM triplekite Algebra 10 December 27th, 2010 10:40 AM Clox Algebra 0 July 1st, 2008 05:55 AM zaserov Applied Math 0 October 24th, 2007 05:39 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top