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October 13th, 2019, 04:05 AM  #1 
Senior Member Joined: Jun 2017 From: Lima, Peru Posts: 178 Thanks: 5 Math Focus: Calculus  How can I find the sum of vectors in this triangle?
The problem is as follows: Using the figure from below find the modulus of the resultant vector if it is known $\left\v\right\=3$ and $\left\u\right\=5$. The alternatives given on my book are: $\begin{array}{ll} 1.&7\\ 2.&10\\ 3.&14\\ 4.&23\\ 5.&28\\ \end{array}$ I tried all sorts of manipulations, and although it doesn't seem complicated the only thing which I could come up with was to find the third side from $\vec{v}$ and $\vec{u}$ which is given from: $\overline{vu}=\sqrt{3^2+5^22(3)(5)\cos\left(120^{\circ}\right)}=7$ But that's where I'm still stuck. I'm confused at how to understand the other two vectors which are not labeled in the question. How am I supposed to sum them with the other two (I mean from the sides of the triangle). Can somebody help me with this?. An answer which would help me the most would be one trigfree and more on the geometric route if possible. This answer may require some drawing please try to include it as I'm slow at translating drawings from words. 
October 13th, 2019, 05:49 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326  Vectors.PNG Let the two vectors without a label be $\vec{a}$ and $\vec{b}$ (as shown above). The resultant of the four vectors can't be found without further information, so I'll assume that $\vec{a}  \vec{v} = \vec{u}  \vec{b}$, which implies $\vec{a} + \vec{b} = \vec{u} + \vec{v}$. Now the resultant vector is $2\left(\vec{u} + \vec{v}\right)$ and has modulus 2*7 = 14. My assumption is equivalent to assuming that the outer segments of the dashed line in the diagram have equal length. 
October 15th, 2019, 10:12 PM  #3  
Senior Member Joined: Jun 2017 From: Lima, Peru Posts: 178 Thanks: 5 Math Focus: Calculus  Quote:
 
October 16th, 2019, 08:47 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,110 Thanks: 2326 
That's right, as the answer depends on the cosine of the given angle. You might prefer a diagram with additional labels, so that the wording "the outer segments of the dashed line" doesn't need to be used.


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