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Find theta from the cross product and dot product of two vectors 
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#1
Feb111, 09:18 PM

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1. The problem statement, all variables and given/known data
If the cross product of vector v cross vector w = 3i + j + 4k, and the dot product of vector v dot vector w = 4, and theta is the angle between vector v and vector w, find tan(theta) and theta. 2. Relevant equations vector c = vw sin(theta) where vector c is the cross product of v and w. 3. The attempt at a solution I'm assuming you have to split the cross product back into the two original vectors and then calculate the angle but I'm not sure how to go from cross product to 2 vectors. Please help! 


#2
Feb111, 09:31 PM

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You can't get the two vectors. And you don't have to.
3i + j + 4k=v*w*sin(theta). 4=v*w*cos(theta). How would you get tan(theta) from that? 


#3
Feb111, 09:36 PM

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#4
Feb111, 09:39 PM

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PF Gold
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Find theta from the cross product and dot product of two vectors
Think trig identity.



#5
Feb111, 09:41 PM

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#6
Feb111, 09:44 PM

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#7
Feb111, 09:45 PM

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#8
Feb111, 09:52 PM

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#9
Feb111, 10:02 PM

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#10
Feb111, 10:06 PM

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So you end up with tan theta = sqrt(26)/4. 


#11
Feb111, 10:07 PM

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then theta = arctan(sqrt(26)/4)
Thanks for the help.. again. 


#12
Feb711, 08:50 PM

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