# Vector..again

• May 3rd 2013, 02:00 AM
Trefoil2727
Vector..again
The angle between vectors a and b is 45. If |a| =5 units and |b| =4 units, find the value of |a-b| and of |a+b|
• May 3rd 2013, 03:33 AM
Plato
Re: Vector..again
Quote:

Originally Posted by Trefoil2727
The angle between vectors a and b is 45. If |a| =5 units and |b| =4 units, find the value of |a-b| and of |a+b|

Think of $\vec{a}~\&~\vec{b}$ as adjacent sides of a parallelogram.
Then $\vec{a}-\vec{b}$ is the diagonal opposite the angle between them.
$\vec{a}+\vec{b}$ is the diagonal opposite the angle adjacent to the angle between them.

Now use the law of cosines.
• May 3rd 2013, 03:33 AM
HallsofIvy
Re: Vector..again
I hope that you know that $|a- b|^2= |a|^2- 2a\cdot b+ |b|^2$ and $|a+ b|^2= |a|^2+ 2a\cdot b+ |b|^2$.

And you should know that $a\cdot b= |a||b|cos(\theta)$ where $\theta$ is the angle between a and b.

I see Plato got in just ahead of me. Different points of view about the same thing.
• May 3rd 2013, 09:08 AM
Trefoil2727
Re: Vector..again
but why a.b=|a||b|cos θ?
• May 3rd 2013, 09:14 AM
Plato
Re: Vector..again
Quote:

Originally Posted by Trefoil2727
but why a.b=|a||b|cos θ?

If you have to ask, then you are in no way ready to do this question.
Why then were you asked to work this question?
• May 3rd 2013, 09:28 AM
Trefoil2727
Re: Vector..again
still can't find a+b..
• May 3rd 2013, 09:32 AM
Trefoil2727
Re: Vector..again
I don't know, maybe my teacher likes to make his students suffer
• May 3rd 2013, 09:46 AM
Trefoil2727
Re: Vector..again
hah, got it! thanks!