## madhu12 Group Title how would we find the unit vector in the direction of v= i+j? 3 years ago 3 years ago

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|=$\sqrt{2}$ 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=$1/\sqrt{2} <1,1>$ or $<1/\sqrt{2}, 1/\sqrt{2}>$ 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=<1,1>.