Linear Algebra - Projection of Vector

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SUMMARY

The discussion centers on the mathematical concept of projecting vector u perpendicular to vector v. The user initially questions the correctness of their answer key, which suggests that the perpendicular component is derived from the equation V - V parallel. After further consideration and analysis, the user acknowledges that the answer key is indeed correct. The key takeaway is the understanding that the projection of a vector involves separating it into parallel and perpendicular components relative to another vector.

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  • Knowledge of vector notation and operations
  • Ability to calculate angles between vectors using the dot product
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YoshiMoshi
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Homework Statement



I feel like this is a easy question but it seems the answer key doesn't seem to be right.

So say I have 2 vectors

equation 1.PNG


and I'm trying to find the projection of vector u perpendicular to the vector v

Homework Equations

The Attempt at a Solution



So I don't remember doing something like this before but I would assume that I start off by finding the projection of u in direction of v

equation 2.PNG

alright so this gives me
equation 3.PNG


So conceptually thinking I see that I have a vector u and a vector V|| sort of like this

IMG_20160408_153526779.jpg

So I can find the angle between u and V and I get 104.963 degrees

IMG_20160408_153856303.jpg


So to get the perpendicular component is it just

tan(theta) = (V perpendicular)/(V parallel)
so V perpendicular is
(V parallel)tan(theta) = V perpendicular?

IMG_20160408_154414914.jpg


I think is conceptually ok but I'm not sure because my answer key does V - V parallel which would appear to be wrong in my opinion because I don't see how that would give us V perpendicular, unless I'm not understanding what vector I'm looking for.

Thanks for any help.
 
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I see that apparently the answer key is correct and see why never mind
 

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