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

Homework Equations

$$||\vec{v} - \vec{w}||^2 = ||\vec{v}||^2 + ||\vec{w}||^2 - 2 ||\vec{v}|| \cdot ||\vec{w}|| \cos \theta$$

The Attempt at a Solution

Isn't [itex]|\vec{AB} + \vec{BC}|[/tex] just [itex]|\vec{AB}| + |\vec{BC}|[/tex]? I mean, isn'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 [itex]|\vec{AB} + \vec{BC}|[/tex]

I mean, mathematically, I believe I can do this:
[itex]|\vec{AB} + \vec{BC}|[/tex] = [itex]|\vec{AC}|[/tex]
Because [itex]\vec{AB} + \vec{BC}[/tex] = [itex]\vec{AC}[/tex]

In which case, [itex]|\vec{AB} + \vec{BC}|[/tex] is intuitive.
But I might be getting myself confused

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 [itex]|\vec{AB} + \vec{BC}|[/tex] = [itex]|\vec{AC}|[/tex]?

If so, why does my teacher insist that I use the cosine law?

 

[Pengwuino]

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

Oh wait wait, my bad, I didn't read those vectors correctly. Disregard my first post.

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]

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

No but ][itex]|\vec{AB} + \vec{BC}|[/tex] and [itex]|\vec{AB}| + |\vec{BC}|[/tex] are related. Question: how?

 

[Дьявол]

$\vec{AB} + \vec{BC}= \vec{CA}$

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

Regards.