What does the last two lines mean? Does u/v mean a quaternion without scalar part or just a vector?
buzz
I also don't undertstand what the last bullet means, especially considering that cross product yields a vector and dot product yields a scalar, and subtraction isn't well-defined between those two objects.
Max
The notation is ambiguously overloaded - on the left u and v are interpreted as quaternions with zero real part and u/v complex part, whereas on the right they are interpreted as R3 vectors. Their cross product gives us the complex part of the resulting quaternion, and the dot product gives us the (negative) real part.
If that doesn't make sense, note that it's saying the same thing as the previous bullet point with a=b=0.
OillyNoodle
The last but two line: u/v --the imaginary part (vector in R3)
The last line: a=b=0
What does the last two lines mean? Does u/v mean a quaternion without scalar part or just a vector?
I also don't undertstand what the last bullet means, especially considering that cross product yields a vector and dot product yields a scalar, and subtraction isn't well-defined between those two objects.
The notation is ambiguously overloaded - on the left u and v are interpreted as quaternions with zero real part and u/v complex part, whereas on the right they are interpreted as R3 vectors. Their cross product gives us the complex part of the resulting quaternion, and the dot product gives us the (negative) real part.
If that doesn't make sense, note that it's saying the same thing as the previous bullet point with a=b=0.
The last but two line: u/v --the imaginary part (vector in R3) The last line: a=b=0