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March 6th, 2016, 09:17 AM   #1
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Simple vector angle question gone wrong

Hello,
I don't even know where to put this question because it's quite basic, but I get a different answer than the one in the book:

I have 2 vectors, AM and AN:
AM=w+0.5u
AN=w+0.5v

Also, |u|=|v|=|w|=1.

What is the angle MAN?

I did (AM<dot>AN)/(|AM|*|AN|) and got that cos(MAN)=0.8, thus MAN=36.86,
but the angle in the book is 25.84, which fits to cos(MAN)=0.9, where is my mistake?

Thank you!
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March 6th, 2016, 09:29 AM   #2
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I agree with your calculation ... maybe a book typo
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March 6th, 2016, 09:46 AM   #3
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Thank you sir
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March 6th, 2016, 12:52 PM   #4
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Could one of you show your working on how you got the angle? I did it and got a different angle, I think I may have missed a step or something
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March 6th, 2016, 01:06 PM   #5
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$\vec{AM} = 0.5u + 0v + w$

$\vec{AN} = 0u + 0.5v + w$

$\vec{AM} \cdot \vec{AN} = (0.5)(0) + (0)(0.5) + (1)(1) = 1$

$|AM| = \sqrt{0.5^2 + 0^2 + 1^2} = \sqrt{1.25}$

$|AN| = \sqrt{0^2 + 0.5^2 + 1^2} = \sqrt{1.25}$

$\cos{\theta} = \dfrac{\vec{AM} \cdot \vec{AN}}{|AM||AN|} = \dfrac{1}{1.25} = 0.8$

$\theta = \arccos(0.8 ) \approx 37^\circ$
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