How do you calculate the magnitude of vectors?

1 Answer

If an accurately drawn scaled vector diagram is used, the magnitude of the vector can be measured using a ruler.


A car travels 120 km east, then turns north and travels another 50 km. What is the displacement of the car?

This could be drawn using carefully drawn vectors, drawn to an appropriate scale such as 1 cm = 20 km. This would mean drawing a 6.0 cm arrow, pointing east, then a 2.5 cm arrow drawn head-to-tail, pointing north (#90^o# angle between). The displacement is the straight-line, "as the crow flies" distance between the starting point and the ending point, which should work out to a 6.5 cm long arrow pointing approximately #23^o# north of east.