Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, indicate whether their velocity vectors are equal or otherwise.

(a) Alice moves north at 6 knots and Bob moves west at 6 knots.

(b) Alice moves west at 6 knots and Bob moves west at 3 knots.

(c) Alice moves northeast at 6 knots and Bob moves south at 3 knots.

(d) Alice moves northeast at 6 knots and Bob moves southwest at 6 knots.

(e) Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.

a) different

b) different

c) different

d) different

e) equal

Explanation:

In order to solve this problem we need to know when two vectors are going to be the same or equivalent. A vector is characterized for having a magnitude and a direction. If two vectors have the same magnitude and direction then they will be the same, no matter where you put them.

a) The two vectors in part a) are different because even though they have the same magnitude they will have different directions.

b) The two vectors in part b) are different because even thougt hey have the same direction they will have different magnitudes.

c) The two vectors in part c) are different because they will have different magnitudes and directions.

d) The two vectors in part d) are different because even though they have theh same magnitude they will have different directions.

e) The two vectors en part e) are the same because they have the same magnitude and direction. One property of vectors is that you can change their position and they will remain the same because they will keep their direction and magnitude.