(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using these 2 vectors:

[itex] \vec u = (3,-4,0)[/itex]

[itex] \vec v = (1,1,1)[/itex]

I must verify that theta is the same with these 2 equations:

Dot product

[itex] \vec u \bullet \vec v = ||\vec u|| ||\vec v|| cos( \theta)[/itex]

Cross product

[itex] ||\vec u \wedge \vec v|| = ||\vec u|| ||\vec v|| sin( \theta)[/itex]

2. Relevant equations

They were given in 1)

3. The attempt at a solution

I did all the calculations, I get the following answers:

[itex] ||\vec u || = 5[/itex]

[itex] ||\vec v || = \sqrt{3}[/itex]

[itex] \vec u \bullet \vec v = -1[/itex]

[itex] ||\vec u \wedge \vec v|| =\sqrt{74}[/itex]

I then solve the 2 equations given above using arcsin and arccos to find the values of theta, but I get 96.6 using the dot product, and 83.3 using the cross product. The weird thing is that 180-83.3 = 96.6...

I must be missing something obvious, but I can't understand why I get the wrong answer :(

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# Angle between 2 vectors using 1) Dot product and 2) cross product gives diff. answer?

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