You are Here: Home >< Maths

# Vectors - C4 watch

1. 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

2. 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.
3. 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
================================ ==================

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: May 10, 2005
Today on TSR

### Four simple steps to get an A*

Here's all you have to do

### 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
Sat, 2 Feb '19
• Sheffield Hallam University
Sun, 3 Feb '19
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams