Find Magnitude of Vectors AB and BC in 2D Space | Vector Addition"

[hahutzy]

Homework Statement

Given:
A (-3,7)
B (5,22)
C (8,18)
are 3 points in 2D space.

Find |\vec{AB} + \vec{BC}|[/tex]<br /> <br /> <h2>Homework Equations</h2><br /> ||\vec{v} - \vec{w}||^2 = ||\vec{v}||^2 + ||\vec{w}||^2 - 2 ||\vec{v}|| \cdot ||\vec{w}|| \cos \theta<br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> Isn&#039;t |\vec{AB} + \vec{BC}|[/tex] just |\vec{AB}| + |\vec{BC}|[/tex]? I mean, isn&amp;amp;#039;t the magnitude of the sum of 2 vectors the same as adding the 2 magnitudes together?

 

[Saladsamurai]

Draw it out and see

 

[hahutzy]

I tried. What I'm confused about is the interpretation of |\vec{AB} + \vec{BC}|[/tex]<br /> <br /> I mean, mathematically, I believe I can do this:<br /> |\vec{AB} + \vec{BC}|[/tex] = |\vec{AC}|[/tex]&amp;lt;br /&amp;gt; Because \vec{AB} + \vec{BC}[/tex] = \vec{AC}[/tex]&amp;amp;amp;lt;br /&amp;amp;amp;gt; &amp;amp;amp;lt;br /&amp;amp;amp;gt; In which case, |\vec{AB} + \vec{BC}|[/tex] is intuitive.&amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;gt; But I might be getting myself confused&amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;gt; &amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;gt; Lastly, my teacher insisted that the cosine law be used, and I have no idea why.

 

[Pengwuino]

Edit: Disregard this post

 

[hahutzy]

So are you saying |\vec{AB} + \vec{BC}|[/tex] = |\vec{AC}|[/tex]?&lt;br /&gt; &lt;br /&gt; If so, why does my teacher insist that I use the cosine law?

 

[Pengwuino]

So are you saying |\vec{AB} + \vec{BC}|[/tex] = |\vec{AC}|[/tex]?

&lt;br /&gt; &lt;br /&gt; Oh wait wait, my bad, I didn&amp;#039;t read those vectors correctly. Disregard my first post.&lt;br /&gt; &lt;br /&gt; Yes, the magnitude of (AB + BC) is equal to the magnitude of AC because the vector AC is the same as the vector you get from adding AB and BC thus it has the same magnitude.

 

[hahutzy]

I still don't understand why I would need to use cosine law for this, as claimed by my teacher...

 

[Pengwuino]

Unless I'm not seeing something, I don't see the need for it. Are you sure you aren't looking for |AC + BC|?

 

[qntty]

|\vec{AB} + \vec{BC}|[/tex] just |\vec{AB}| + |\vec{BC}|[/tex]

&lt;br /&gt; &lt;br /&gt; No but ]|\vec{AB} + \vec{BC}|[/tex] and |\vec{AB}| + |\vec{BC}|[/tex] are related. Question: how?

 

[Дьявол]

<br /> \vec{AB} + \vec{BC}= \vec{CA}<br />

So, you need to find |\vec{-AC}|=|\vec{AC}|

Regards.