ECZ 2022 · O-Level Paper 2 · Question 2 — Vectors In Two Dimensions
In the parallelogram OABC, OA = 4a, OC = 6c, AP = (23)AC and M is the midpoint of BC.
(a) Solve the equation 3x2 - 5x - 7 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
a = 3, b = -5, c = -7(b(i)(a)) In the parallelogram OABC, OA = 4a, OC = 6c, AP = (23)AC and M is the midpoint of BC. Find AC in terms of a andorc.[1]
Verified working — step 1
AC = OC - OA = …(b(i)(b)) Find OP in terms of a andorc.[1]
Verified working — step 1
OP = OA + AP = 4a + (23)(6c - 4a)(b(i)(c)) Find OM in terms of a andorc.[1]
Verified working — step 1
In the parallelogram, OB = OA + OC = …(b(ii)) Hence or otherwise, show that the points O, P and M are collinear.[2]
Verified working — step 1
OP = (43)a + 4c and OM = 2a + 6c.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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