Supplementary Worksheet

Supplementary worksheet: Vectors 1. Let ABCD be a parallelogram. a. Place I and J such that :

uuu r 1 uuur BI = AB 3

and

uuur uuuu r AJ = 4AD

.

b. Show that C, I and J are collinear. 1.

Given three points A, B and C. Let M be a point in the plane defined by:

uuuu r uuuu r uuuur uuur MA + 3MB = 2MC + 2AB

I be the midpoint of [AB]. Show that:

and let

uuur uuuu r MI = AC

2. Consider in a plane, the four points A, B, C and D. a. Construct the point M such that: uuuur uuur uuuu r uuur AM = AB + AC − BC b.

Construct the point N such that:

c.

Show that:

uuuu r uuur uuuu r uuuu r AN = AB − AC + AD

uuuur uuuu r uuur NM = AC + DB

1. Given a triangle ABC and let L, M and N be three points defined by: uuur uuur r 2LB − 3LC = 0 uuuu r uuuur r MA + 3MC = 0 uuur uuur r NA + 2NB = 0

a. Show that:

uuur uuur BL = 3BC uuuur 3 uuuu r AM = AC 4 uuuu r 2 uuur AN = AB 3 b.

Express

c.

Show that

uuuur MN

in terms of

uuur AB

and

uuuu r AC

uuur 1 uuur uuur NL = AB + 3BC 3

d. Show that L, M and N are collinear.

5. Let ABC be a triangle, D and E are points defined by: uuuu r uuur 1 uuuu r AD = BA + AC 2 uuur 1 uuuu r AE = AC 4

Show that the points B, D and E are collinear. 6. ABC is a triangle and D be a point defined by: uuuu r uuuu r 1 uuur AD = 3AC + CB 2

Show that

uuur uuur 5 uuur BD = −2BA + BC 2