PQRS is a parallelogram with P->Q=a and P->S=b. Find S->Q in terms of a and b. N is a point between S and Q, where SN:NQ is 3:2, find N->R

Vectors are special in that they have a direction as well as magnitude (size).

To get from S->Q you can go from S->P = -b and then P->Q =a so S->Q = -b + a = a-b (remember underlining)

To find N->R break it down into N->Q + N->R

S->Q is made of 5 parts namley 3 in S->N and 2 in N->Q, so N->Q must equal a 2/5 of S->Q and we know S->Q

Q->R = b

so in total N->R = 2/5(a-b) + b