Suppose you take two non-zero displacements represented by vectors A & B. The magnitude of A is 5 m and the magnitude of B is 6 m. Under what circumstances can you end up back at your starting point? What is the magnitude of the largest displacement you can end up from the starting point? Suppose you take two non-zero displacements represented by vectors A & B which are perpendicular to each other. The magnitude of A is 5 m and the magnitude of B is 6 m. What is the component of vector B along the direction of vector A measured in m?

a. When the total displacement is -(A + B)

b. A + B = 1 m or -(A + B) = -11 m

c. 0 m

Explanation:

a. Under what circumstances can you end up back at your starting point?

If we have the displacement A and displacement B. The total displacement is A + B. We would end up at the starting point if we take a displacement -(A + B) from point B

b. What is the magnitude of the largest displacement you can end up from the starting point?

The maximum displacement we can obtain is when A and B are in the same direction. So A + B = 5 m + 6 m = 11 m or -A - B = -(A + B) = -11 m.

c. When A and B are perpendicular, what is the component of B in the direction of A?

Since A is perpendicular to B, the angle between A and B is 90°

So the component of B in A,s direction is Bcos90° = B × 0 = 0 m