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Projections

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Anonymous User
Projections
September 10, 2006 12:21PM
Anyone know where they get W.v = &v.v + u.v = &v.v on page 731?

Thanks
Re: Projections
September 11, 2006 10:13PM
start with: w = &.v + u
you can get this from plain vector addition of the the parallel (&.v) and orthogonal (u) components of w. or the "triangle rule" if you prefer.

then multiply both sides by v, for no good reason other than to get the result: w.v = &.v.v + u.v

now the u.v = 0 part comes into play - you can substitute u.v in the previous equation with zero, giving you w.v = &.v.v as advertised. As it says in the textbook, u.v = 0 because u and v are defined as being orthogonal and the dot product of two orthogonal vectors is zero.
Anonymous User
Re: Projections
September 12, 2006 03:37PM
for the statement

"then multiply both sides by v, for no good reason other than to get the result: w.v = &.v.v + u.v"

Vector dot product is not the same as vector multiplication.

But Would that mean you take the dot product of both sides?


Re: Projections
September 13, 2006 08:37AM
I guess so. I kindof equated the two statement like I would have in highschool: multiply both sides by the same thing and the equality holds. I don't know my math well enough to know if taking the dot product on both sides yields the same result, but it certainly looks that way.
Anonymous User
Re: Projections
September 13, 2006 12:25PM
Re: Projections
September 17, 2006 09:48AM
Any idea why on p271 they chose to use P=ST instead of P=TS, which is simpler? i.e. are they not equivalent?

also. on p248 do you think that when they say the plane formed by n and v_up that they mean the plane formed by the point vrp and these two vectors? and if so how is that different from the plane that we're trying to find a reference frame for? and if it is different why should v lie in that plane. and why should v be a linear combination of n and v_up because of this? and why can we set beta=1?
Anonymous User
Re: Projections
September 18, 2006 05:55PM
dont think we have to know this

I think we have to know the assignment maths , maths in the tutorials and the appendixes.

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