Pythagorean vectors If you walk 40 m east and then 30 m north, how far from the starting point are you?
A. 10 m
B. 50 m
C. 70 m
The two legs of your trip form the sides of a right triangle; your final displacement is the hypotenuse. Draw a diagram showing the two successive displacements and the vector sum. You can use the Pythagorean theorem to calculate the length of the vector sum, 50 m.
You can confirm the length of this resultant vector by using what you know about parallel and antiparallel vectors. If the two legs of your trip were antiparallel (rather than at right angles), the resultant would have a magnitude of 10 m. So answer A can’t be right; the correct answer must be larger. If the two legs were parallel (i.e., if you walked 40 m and then continued 30 m in the same direction), the resultant would have a magnitude of 70 m, so answer C can’t be right either; the correct answer must be smaller. That leaves B as the correct answer.