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October 13th, 2019, 04:08 AM   #1
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Question 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.
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October 13th, 2019, 07:02 AM   #2
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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.
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October 15th, 2019, 10:15 PM   #3
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Question A drawing please?

Quote:
Originally Posted by skipjack View Post
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.
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October 16th, 2019, 09:35 AM   #4
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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, $\vec{MA} + \vec{MB} = 2\vec{MN}$.
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