A jogger travels a route that has two parts. The first is a displacement A of magnitude 2.70 km due south, and the second involves a displacement B that points due east.


What is the direction of A + B relative to due south?
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What would be the direction of A - B relative to due south?

To find the direction of A + B relative to due south, you need to find the resultant displacement vector by adding vectors A and B. Draw a diagram to visualize the displacement vectors.

1. Draw an arrow representing a displacement of magnitude 2.70 km due south (A).
2. From the end of vector A, draw another arrow representing a displacement due east (B).
3. Connect the initial point of vector A to the end point of vector B.
4. The resultant vector represents the sum of vectors A and B.

To determine the direction of the resultant displacement vector (A + B) relative to due south, measure the angle it forms with the due south direction.

To find the direction of A - B relative to due south, you also need to find the resultant displacement vector, but this time by subtracting vector B from vector A.

1. Draw an arrow representing a displacement of magnitude 2.70 km due south (A).
2. From the end of vector A, draw another arrow representing a displacement due east (B), but now in the opposite direction (opposite to the original B).
3. Connect the initial point of vector A to the end point of the new vector B (which is in the opposite direction).
4. The resultant vector represents the difference of vectors A and B.

To determine the direction of the resultant displacement vector (A - B) relative to due south, measure the angle it forms with the due south direction.