Question worth 5 marks....

Referred to a fixed origin O, the position vectors of the points P and Q are (6i – 5j) and (10i + 3j) respectively. The midpoint of PQ is R.

(a) Find the position vector of R

The midpoint of OP is S.
(b) Prove that SR is parallel to OQ

OP = 6i – 5j
OQ = 10i + 3j

a)

PQ = (10i + 3j) - (6i - 5j) = 4i + 8j


OR = OP + ½ PQ = (6i - 5j) + (2i + 4j) = 8i - j

or

OR = OQ - ½ PQ = (10i + 3j) - (2i + 4j) = 8i – j

b)

OS = ½ OP = 3i - 2.5j

SR = OR - OS = (8i - j) - (3i - 2.5j) = 5i + 1.5j = ½ OQ

-