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Please give me a hint to solving this simple vector dot product proof 
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#1
Feb1212, 05:50 PM

P: 116

1. The problem statement, all variables and given/known data
Let 'u' and 'v' be two non zero vectors such that the prjection of 'u' along 'v' equals the projection of 'v' along 'u.' Using the formula for projection, show that 'u' and 'v' are either perpendicular or parallel. 2. Relevant equations 3. The attempt at a solution Please don't just answer it, I would like to do this one on my own. But I first need a hint because I have been trying for about 30 minutes. I know that the projection of 'u' along 'v' is u dot v, divided by the square of the norm of 'v'. Then this scalar is multiplied through 'v'. But that's about all I have. Edit: I guess I said more about how far I got. I get the following: [itex]\frac{1}{v^{2}}[/itex][itex]\overline{v}[/itex]=[itex]\frac{1}{u^{2}}[/itex][itex]\overline{u}[/itex] 


#2
Feb1212, 08:57 PM

HW Helper
Thanks
PF Gold
P: 7,662

\vec A\cdot \vec B = \vec A\vec B\cos\theta$$implies about this problem. 


#3
Feb1412, 01:35 PM

P: 116

(sorry for the long time before replying)
Thanks! That hint definitely helped me out! In case anyone comes by this thread seeking the same as I did, when you apply the identity that LCKurtz showed us, you get a scalar number multiplied by vector v equals vector u. Obviously, this means they are either parallel or antiparallel. 


#4
Feb1412, 02:00 PM

HW Helper
Thanks
PF Gold
P: 7,662

Please give me a hint to solving this simple vector dot product proof



#5
Feb1412, 02:18 PM

P: 116

But then wouldn't that just mean that they are parallel anyways? So no matter how you look at it, if proj u over v equals proj v over u, as long as these aren't zero vectors, wouldn't the angle HAVE to be 0 or 180?



#6
Feb1412, 02:22 PM

HW Helper
Thanks
PF Gold
P: 7,662




#7
Feb1412, 02:26 PM

P: 116

Definitely one vector dotted into another equals 0 if they are both perpendicular. Thanks again! 


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