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 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
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Math Focus: Calculus A drawing please?

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 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 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

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