9. In the diagram, OABC is a parallelogram. The point D lies on BC produced such that CD = 3BC. AD intersects OC at E. E -> (a) Given that OA = -> 2p and OC = 3q, %3D %3D find, in terms of p and q, the vectors 之 (ii) AC, -> -> (i) ОВ, -> (b) Given that AE = A AD, deduce the value of 2. Evaluate the ratio OE : EC and show that -> EB = OC + DA. oc 4

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 21E
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9. In the diagram, OABC
is a parallelogram.
The point D lies on
BC produced such
that CD = 3BC. AD
C
%3D
intersects OC at E.
->
(a) Given that OA =
->
2p and OC = 3q,
%3D
find, in terms of p
and q, the vectors
->
(i) OB,
(ii) AC,
->
->
(b) Given that AE = A AD, deduce the value of
2. Evaluate the ratio OE : EC and show that
EB = OC +
->
DA.
4
%3D
29
Transcribed Image Text:9. In the diagram, OABC is a parallelogram. The point D lies on BC produced such that CD = 3BC. AD C %3D intersects OC at E. -> (a) Given that OA = -> 2p and OC = 3q, %3D find, in terms of p and q, the vectors -> (i) OB, (ii) AC, -> -> (b) Given that AE = A AD, deduce the value of 2. Evaluate the ratio OE : EC and show that EB = OC + -> DA. 4 %3D 29
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