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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: Orthogonality''
by darkgently on 2009-11-24 15:01:49 |
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| > I know how to find the norm(length) of each vector. The
> norm of <1, ,1 ,1> is 3 and the norm of <1 , -1 ,0 > is 2.
Actually, those norms are the square root of 3 and the square root of 2 respectively.
> Would I need 3 vectors for the basis in R^3?
Of course. Every basis for R^n has n vectors. That's how the dimension of a vector space is defined: the number of vectors in a basis.
> I need to teach myself the cross product.
Yes, it's important because the cross product of any two vectors is orthogonal to both. You can start with our article here: http://planetmath.org/encyclopedia/CrossProduct.html
> To find a basis could I normalize each vector ?
You need a third vector, linearly independent to the other two. In this case your two given vectors are already orthogonal, so if you let the third vector be their cross product you will have a mutually orthogonal set of 3 vectors. Then, as you say, you can normalise each vector to obtain an orthonormal basis for R^3.
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