1. Sketch the following vectors and use Pythagoras' Theorem to find the length (magnitude) of each to 2 significant figures:

2. Give the matrix (bracket) form of the following vectors. Each square is one unit.






3. Draw the following vector triangles and write down the resultant vector:







4. ABCD is a parallelogram.


(a) Give a vector equal to .

(b) Complete  = ________

(c) True or false? 

(d) Complete __________

(e) Complete  = __________





5. The figure shows the vector , without an arrow!

Copy and complete a vector triangle to illustrate the vector sum:


6. A plane sets off on a couse of 090° (East) at a speed in the air of 300 km/h. A wind of speed 50 km/h is blowing from the south (180°).

a. Draw a vector triangle to show the actual path of the plane.

b. Use a scale drawing to find the bearing of the planes flight.



A cyclist can pedal downhill at 35 km/h

He is cycling down a straight mountain road in a southerly direction.

The wind is blowing from the west at 10 km/h.

Draw a vector diagram to illustrate this and then use it to find the cyclist's actual speed.


8. Ron the runner runs in a marathon and is heading due North.

His speed in still air is 15 km/h.

He has the wind behind him from the South at a speed of 5 km/h.

What would his actual speed be?



Jung-Min is a swimmer and is swimming from Mission Bay in Auckland to Rangitoto Island. He can swim at 3 km/h in still water. The current is directly from the side and is 1 km/h.

Draw a vector traingle to scale and a scale drawing to find his swimming speed.


10. A windsurfer does the same trip as Jung-Min in question 9. On a windy day for her journey the wind is directly behind and blowing at 25 km/h and the current is directly from the side at 4 km'h.

Draw a vector triangle and a scle drawing to find her speed.