angle between displacement vectors

**ohdearthisisheadrot** · March 17th 2009, 10:55 AM

Hi,

what is the angle between these vectors?

u=(1, -1, sqrt 6) and v = (-1, 1, sqrt 6)

I used cos theta = a.b/ |a| |b| to get 87.9 degrees but on the multi choice question this isnt one of the answers and i cant see where ive gone wrong.

Cheers!

**running-gag** · March 17th 2009, 11:15 AM

Originally Posted by ohdearthisisheadrot

Hi,

what is the angle between these vectors?

u=(1, -1, sqrt 6) and v = (-1, 1, sqrt 6)

I used cos theta = a.b/ |a| |b| to get 87.9 degrees but on the multi choice question this isnt one of the answers and i cant see where ive gone wrong.

Cheers!

Hi

$\cos \theta = \frac{\overrightarrow{u}.\overrightarrow{v}}{||\ov errightarrow{u}||.||\overrightarrow{v||}}=\frac{1\ cdot(-1) + (-1)\cdot 1 + \sqrt{6}\cdot \sqrt{6}}{\sqrt{1^2+(-1)^2+\sqrt{6}^2}\cdot \sqrt{(-1)^2+1^2+\sqrt{6}^2}}$

$\cos \theta = \frac{4}{\sqrt{8}\:\sqrt{8}}= \frac{4}{8}=\frac12$

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