Question

The vector rotation sign
is​

Answer 1

It can be positive or negative depends on the "direction" of your rotation axis. The convention is the right hand rule.

If you point your thumb in the "direction" of your rotation axis and you index finger to the direction of the 1st vector. If you can point your middle finger to the direction of the 2nd vector, then the rotation is considered to be positive. If not, then the rotation is considered to be negative.

In ordinary R3, the "positive directions" of the 3 axis is setup such that if you rotate the vector in "positive direction" of x-axis with respect to the "positive direction" of z-axis for 90∘, you get a vector in the "positive direction" of y-axis.

R³ is ur final answer.

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