How would we find the unit vector in the direction of v = i+j?

The vector i = and j = so the i+j==. The length of this vector is easy: |i+j| = 2-√ to make the vector i+j = a unit vector we rescale it by it's length (i. e. divide i+j by its length), v = (i+j) / (|i+j|) thus we have v = 1 / 2-√ or <1 / 2-√,1 / 2-√ > If you check the length of this vector v, you see it indeed does have length = 1. It is parallel to the vector i+j because it's components are proportional to the components of i+j=.