Supplementary Worksheet 2 Vectors

Supplementary Worksheet 2 Chapter 8: Vectors

1.

ABC is a triangle. a. Construct the points I and J such that: and . uuu r uuur uuuu r AI = AB + AC

uuur uuur uuuu r AJ = AB − AC

b. Deduce that B is the midpoint of [IJ]. 1. ABCD is a parallelogram. a. Construct the points I and J such that

and

uu r 1 uuur IJ = BA 2

uuu r r 1 uuuu AI = − AD 2

.

b. Show that A, C and J are collinear. 1. ABC is a triangle. a. Construct the points D and E such that

and b.

uuur uuur uuuu r AE = 2AB + AC

Express and

uuur 1 uuur BD = BC 3

uuur BC

uuuu r AD

and

uuur AE

as linear combinations of

uuur AB

.

c. Deduce that the points A, D, and E are collinear. 1. Let ABC be a triangle.

a. Construct the points E, F and G such that: uuur 1 uuur AE = AB 2 uuur uuur AF = 2CF uuur uuur r 2GE + GC = 0 b.

Show that

c.

The line (AG) cuts (BC) in K. What does K represent with respect to [BC].

uuur uuur BF = 2EC