Question 8:
Diagram 3 shows a parallelogram OABC. Point P is the midpoint of AB and the ratio of →QP:→OP=2:5.Given that →OA=3i˜+4j˜ and →OC=6i˜+j˜
Diagram 3
Express in the terms of i˜ and j˜,(a) →OP (1 mark)(b) →AQ (3 marks)
Solution:
(a)
→OP=→OA+→AP =3i˜+4j˜+12(→AB) =3i˜+4j˜+12(→OC) =3i˜+4j˜+12(6i˜+j˜) =3i˜+4j˜+3i˜+12j˜ =6i˜+92j˜
(b)
→QP:→OP=2:5→QP→OP=25→QP=25×→OP→AQ=→AO+→OQ =−→OA+(35×→OP) =−(3i˜+4j˜)+35(6i˜+92j˜) =−3i˜−4j˜+185i˜+2710j˜ =35i˜−1310j˜
Diagram 3 shows a parallelogram OABC. Point P is the midpoint of AB and the ratio of →QP:→OP=2:5.Given that →OA=3i˜+4j˜ and →OC=6i˜+j˜

Express in the terms of i˜ and j˜,(a) →OP (1 mark)(b) →AQ (3 marks)
Solution:
(a)
→OP=→OA+→AP =3i˜+4j˜+12(→AB) =3i˜+4j˜+12(→OC) =3i˜+4j˜+12(6i˜+j˜) =3i˜+4j˜+3i˜+12j˜ =6i˜+92j˜
(b)
→QP:→OP=2:5→QP→OP=25→QP=25×→OP→AQ=→AO+→OQ =−→OA+(35×→OP) =−(3i˜+4j˜)+35(6i˜+92j˜) =−3i˜−4j˜+185i˜+2710j˜ =35i˜−1310j˜