Vector

(a) PS = PR + RS = a - 3b + b = a - 2b.
QR = QP + PR = a + a - 3b = 2a - 3b.
(b)
PS/PT = 1/h, so PT = hPS = h(a - 2b) = ha - 2hb......(1) h = lambda.
QR/QT = 1/k, so QT = kQR = k(2a - 3b) = 2ka - 3kb ...(2) k = mu.
Let O be the origin, let OP = p and let OQ = q.
So OT = OP + PT = p + ha - 2hb ................(3)
Also, OT = OQ + QT = q + 2ka - 3kb ............(4)
But OP = OQ + PQ =
so p = q + a, sub. into (3), we get
OT = q + a + ha - 2hb = q + (1 + h)a - 2hb.......(5)
Comparing (4) and (5),
2k = 1 + h ................(6) and
- 3k = - 2h .................(7)
Solving (6) and (7), we get
k = mu = 2 and h = lambda = 3.