a x b = |a| |b| sin(θ) n, where θ is angle between a and b and n is a unit vector perpendicular to both in direction determined by right hand rule. So if the two vectors are the same, then the angle is 0 and the sine is 0. E.g., i × i = 1*1*sin(0) = 1*0 = 0. Instead of right hand rule you can use signed angles. CCW in x-y plane is positive, CCW in y-z plane is positive, and CCW in z-x plane is positive. i × k = 1*1*sin(–90°) j = 1*1*(–1) j = – j.
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