The vector i=<1,0> and j=<0,1> so the i+j=<1+0,0+1>=<1,1>. The length of this vector is easy: |i+j|=<span>2–√</span>
to make the vector i+j=<1,1> 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=<span>1/<span>2–√</span><1,1></span> or <span><1/<span>2–√</span>,1/<span>2–√</span>></span>
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=<1,1>.
