In the following diagram, OA = a, OB = b. C is the midpoint of [OA] and OF (a) Find, in terms of a and b () OF; (i) AF. It is given also that AD = 1. AF and CD = uCB, where i, ueR. (b) Find an expression for (1) OD in terms of a, b and à; (ii) OD in terms of a, b and u. (c) Show that , and find the value of . (d) Deduce an expression for CD in terms of a and b only. 6.
In the following diagram, OA = a, OB = b. C is the midpoint of [OA] and OF (a) Find, in terms of a and b () OF; (i) AF. It is given also that AD = 1. AF and CD = uCB, where i, ueR. (b) Find an expression for (1) OD in terms of a, b and à; (ii) OD in terms of a, b and u. (c) Show that , and find the value of . (d) Deduce an expression for CD in terms of a and b only. 6.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![In the following diagram, OA = a, OB = b. C is the midpoint of [OA] and OF
(a) Find, in terms of a and b
()
OF;
(i) AF.
It is given also that AD = 1. AF and CD = uCB, where i, ueR.
(b) Find an expression for
(1)
OD in terms of a, b and à;
(ii) OD in terms of a, b and u.
(c) Show that
, and find the value of .
(d) Deduce an expression for CD in terms of a and b only.
6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6accde57-4151-4a64-887a-ef329464b649%2F9740e103-f601-4601-baba-82ddfd187096%2F2cdc30j_processed.png&w=3840&q=75)
Transcribed Image Text:In the following diagram, OA = a, OB = b. C is the midpoint of [OA] and OF
(a) Find, in terms of a and b
()
OF;
(i) AF.
It is given also that AD = 1. AF and CD = uCB, where i, ueR.
(b) Find an expression for
(1)
OD in terms of a, b and à;
(ii) OD in terms of a, b and u.
(c) Show that
, and find the value of .
(d) Deduce an expression for CD in terms of a and b only.
6.

Transcribed Image Text:The vectors a and b are defined by a =
where teR.
41
(a) Find and simplify an expression for a ·b in terms of r.
(b) Hence or otherwise, find the values of i for which the angle between a and b is obtuse.
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