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Finding an orthogonal vector

by rocketman123
Tags: orthogonal, vector
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rocketman123
#1
Mar19-10, 03:24 PM
P: 1
Hey guys,

Given a vector, ie < -1, 2, 3 > , how does one go about finding a vector which is orthogonal to it?

I also have another vector < x, y ,z > which is the point of origin for the above vector.

In context, I'm given a directional vector from which I need to find an 'up' vector and a 'horizontal' vector. You can see here http://www.cs.auckland.ac.nz/~jli023...glechanged.jpg - I have a 'look_at' vector and must determine a suitable up and right vector.

I know that to get the right/ horiztonal vector I can just take the cross product between the directional / look at vector and the up vector. However, how to get the up vector confuses me.

A standard up vector is <0 1 0 >. Would it make sense to take the cross product of <0 1 0 > and the direction vector - to get the horizontal vector. And then take the cross product of the horizontal and directional vectors to get the proper up vector? It makes sense to me, however I have no real way of checking if my answer is correct! - I need to find some nice 3d plotting software hehe

Cheers,
Dan
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tiny-tim
#2
Mar20-10, 04:02 PM
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tiny-tim's Avatar
P: 26,148
Hi Dan! Welcome to PF!

I'm confused surely all up vectors are the same?

(and not orthogonal to the 'look at' vector)


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