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HELP!: Vectors Math Problem!
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+Karma for anyone who can do/help me figure this question out.
1. Find a vector parallel to the same plane that is parallel to
vector a=[3,-4,2] and vector b=[6,-5,1]. It MAY NOT be parallel to either of the aforementioned vectors.
This is a TIPS assignment which I pretty much figured out until this question, keep in mind we have used cross product, dot product very often in this class and I know we need to use both these equations to solve. Thanks!
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i'm learning vectors now, but not this in depth. so anyways, free bump.
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i dunno im taking algebra its so boring...
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maybe im a dumbo but it asks to find a parallel vector to the two vectors, then says it cant be parallel? im lost.
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It is parelell to the same plane as the other two vectors but not the exact plane.
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You just take the cross product of the 2 vectors. Cross product = vector normal to the plane made by 2 vectors. I think the answer is [6,-9,9] but I just tried that in my head so double check.
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The first thing you do is cross product but that only gives you a vector that runs perpendicular out of A and B
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Right, but that new vector is in another plane right? So if you take the cross product of some made up vector in the new plane, you will get a vector parallel to the first plane, but not the given vectors. It would be easier if I could show you but I hope that helps.
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I think I can manage that, thanks for the help man ill work it out
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First you need to find a vector normal/orthogonal to the plane. To do this, take the cross product of your two vectors. I think you already know how to do that.
Once you find the normal vector, n, setup an equation using any point on the previous plane. So, say you have the following:
n = ai +bj + ck. This should be familiar to you.
Take a point, P(D,E,F). You then setup the equation:
a(x-D) + b(y-E) + c(z-F) = 0.
Then you solve it so that you get an equation that looks like:
ax + by + cz = aD + bE + cF
and example of the final plane would look like:
4x + 2y - 3z = 12 or something, I just made that up. If you have any questions feel free to ask.
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