# Math Help - Angle between 2 vector

1. ## Angle between 2 vector

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

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

Is dont know what to do afterwards???

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

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

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

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

5. 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.

6. 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?