Angle between 2 vector

**zorro** · December 28th 2009, 11:16 PM

Question : If $2 \theta$ is the angle between the 2 unit vectors $\bar a$ and $\bar b$ , then show that $|\bar a - \bar b| = 2 sin \theta$
-----------------------------------------------------------------------
Solution:

I know $\bar a - \bar b = |\bar a ||\bar b| cos \theta$

Is dont know what to do afterwards???

**CaptainBlack** · December 29th 2009, 12:50 AM

Originally Posted by zorro

Question : If $2 \theta$ is the angle between the 2 unit vectors $\bar a$ and $\bar b$ , then show that $|\bar a - \bar b| = 2 sin \theta$
-----------------------------------------------------------------------
Solution:

I know $\bar a - \bar b = |\bar a ||\bar b| cos \theta$

Is dont know what to do afterwards???

Draw a diagram then it is simple geometry.

CB

**zorro** · December 29th 2009, 12:58 AM

CB i dont know how to draw a diagram with so little ......

angle is 2 tita how should i dram that.........

**Shanks** · December 29th 2009, 01:58 AM

Notice that
$\left|\bar a-\bar b\right|^2=<\bar a-\bar b,\bar a-\bar b>$

**Sudharaka** · December 29th 2009, 02:29 AM

Dear zorro,
This is a method which does not require any geometrical drawing. But I think sometimes you will find this method an interesting one. Sorry,I did'nt have time to type the answer. If you have any questions please don't hesitate to ask me.

**Grandad** · December 29th 2009, 02:45 AM

Hello zorro

Originally Posted by zorro

CB i dont know how to draw a diagram with so little ......

angle is 2 tita how should i dram that.........

Have a look at the attached drawing.

Since $\textbf{a}$ and $\textbf{b}$ are unit vectors, $|PQ| = |PS| = 1$ , and $|\textbf{a}-\textbf{b}| = |QS|$ .

Can you complete it now?

Grandad

**zorro** · December 29th 2009, 12:24 PM

Thanks Sudharaka and grandad and also every one for ur answer.....

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