Rotate a 3D point around the origin / tilt a 3D vector?

Let's say you have a vector v1. First, you should find a vector v2 which is perpendicular to v1. Then the vector you want to find out is half between v1 and v2, that is v3 = norm(norm(v1)+norm(v2)) .

And how to find v2? You can take a cross product of v1 and any vector which is not parallel to v1. So you can do something like this.

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