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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.

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
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.
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.
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.
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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