During a relay race, runner A runs a given distance due north and then hands off

Question

During a relay race, runner A runs a given distance due north and then hands off the baton to runner B, who runs for the same distance in a south easterly direction. The two displacement vectors are shown in the drawing. Are they equal?

====Im leaning toward answer C, but i got confused with the wording "they must have the same magnitude"===, which makes make think of answer A.



A)Yes, because distances traveled by the two runners are the same.

B)Yes, because the distances traveled by the two runners are the same, and the tail of B meets the head of A, as it must in tail-to-head addition.

C)No, because for two vectors to be equal, they must have the same magnitude and point in the same direction.

D)No, because for two vectors to be equal, the tails of both vectors must start at the same location.

Explanation / Answer

You are right, the answer is C.

Two vectors are equal only if they have the same magnitude and direction.

Another way to look at it is the vectors must have the same x and y components. They will have much different components because of the different direction.

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