unit vector notation

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soccerball3211

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May 16, 2005
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In the product vector F = q vector v × vector B, take q = -3,

vector v = 2(i hat) + 4(j hat) + 6(k hat)
vector F = 4(i hat) - 20(j hat) + 12( k hat)
What then is in unit-vector notation if Bx = By ?

Can someone please help me get started with this problem?
 
what are x and y in the final question? and B isn't given, so are you trying to solve for vector B?
 
okay, but what is the x y? i'm confused, because you have three dimensional vectors, so if the problem is trying to say that the answer must be a unit vector, why doesn't it say Bx=By=Bk?

and is the x in the problem referring to the cross product? if so i would write 4i-20j+12k= -3 (2i+4j+6k x B). if -3 is a scalar, i think you can then move it to the other side, but i am not sure. then i think you can either solve that by hand or with a calculator.
 
yes, but if it's a cross product you can't really isolate it. i have used calculators to solve for cross products, i think that you might need to do this by hand.
 
can I move the -3 to the other side of the equals sign and if I do that what good will it serve?
 
yes, as -3 is a scalar, i am fairly certain you can divide it into the other side. it might make it easier to solve for B if you see what the result of your cross product should be exactly.
 
i am not sure how to do it on a calculator. dividing a vector by a scalar leaves you another vector. that is also how you obtain unit vectors (dividing by the magnitude). so you just divide as you normally would.
 
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