Turn on thread page Beta
    • Thread Starter

    Done (i), got idea how to do (ii), by can't really get the way round it, please help...... :P

    As shown in the diagram the points A and B have position vectors a and b with respect to the origin O.

    (i) Make a sketch of the diagram, and mark the points C, D and E such that OC=2a, OD=2a + b and OE = 1/3(OD).

    (ii) By expressing suitable vectors in terms of a and b, prove that E lies on the line joining A and B.
    Attached Images

    OE = (1/3) OD = (2a+b)/3

    AE = AO + OE = -OA + OE = -a + (2a+b)/3 = (b-a)/3
    BE = BO + OE = -BO + OE = -b + (2a+b)/3 = 2(b-a)/3

    Since AB = (b-a), then E divides the line AB into the ratio 1:2.

    let r be the line joioning A and B

    r = OA + λAB
    r = a + λ(b - a)
    r = a(1 - λ) + λb

    OE = (1/3)OD
    OE = (1/3) (2a + b)
    OE = (2/3)a + (1/3)b
    OE = a(1 - 1/3) + (1/3)b = a(1 - λ) + λb for λ = 1/3

    i.e E lies on the line r.
    A is the point on r at which λ = 0
    B is the point on r at which λ = 1

    Since λ = 1/3 is between λ = 0 and 1, then E lies between A and B
    ================================ ==================
Turn on thread page Beta
Updated: May 10, 2005

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19
  • Sheffield Hallam University
    City and Collegiate Campus Undergraduate
    Sun, 3 Feb '19
Brexit: Given the chance now, would you vote leave or remain?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way


Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.