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|

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- May 3rd 2013, 02:00 AMTrefoil2727Vector..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 AMPlatoRe: Vector..again
Think of $\displaystyle \vec{a}~\&~\vec{b}$ as adjacent sides of a parallelogram.

Then $\displaystyle \vec{a}-\vec{b}$ is the diagonal opposite the angle between them.

$\displaystyle \vec{a}+\vec{b}$ is the diagonal opposite the angle adjacent to the angle between them.

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

And you should know that $\displaystyle a\cdot b= |a||b|cos(\theta)$ where $\displaystyle \theta$ 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 AMTrefoil2727Re: Vector..again
but why a.b=|a||b|cos θ?

- May 3rd 2013, 09:14 AMPlatoRe: Vector..again
- May 3rd 2013, 09:28 AMTrefoil2727Re: Vector..again
still can't find a+b..

- May 3rd 2013, 09:32 AMTrefoil2727Re: Vector..again
I don't know, maybe my teacher likes to make his students suffer

- May 3rd 2013, 09:46 AMTrefoil2727Re: Vector..again
hah, got it! thanks!