Find out how long the vector is. This vector is too short. We want it to have length 1, but it only has length . P If we multiply the vector by 2, we'll get a new vector with magnitude 1. Let
The magnitude of *v* is Therefore *v* is a unit vector, which is what we wanted. Remember your fraction division: multiplying by 2 is the same thing as dividing by . We found the normalization of . Since multiplying by 2 is the same thing as dividing by , we could also write the vector as which happens to be the same thing as If we're given a vector *v* and asked to normalize it, find the vector This is guaranteed to be a unit vector pointing in the same direction as *v* (unless *v* is 0, but that's not a vector). What direction does <0,0> point?. It doesn't. |