Final answer:
The resultant vector A + B has a magnitude of approximately 158.39 units and is directed 45° south of west. The resultant vector A - B also has a magnitude of 158.39 units but is directed 45° north of west.
Step-by-step explanation:
Vector Addition and Subtraction
To find the magnitude and direction of the vectors A + B and A - B, we use vector addition and subtraction rules. Since vector A has a magnitude of 79 units and points due west, and vector B has the same magnitude and points due south, we can represent them as perpendicular vectors in a coordinate system with A along the negative x-axis and B along the negative y-axis.
For vector A + B, we place B's tail at A's head, forming a right-angled triangle. The magnitude of the resultant vector R can be calculated using the Pythagorean theorem:
R = √(A^2 + B^2) = √(79^2 + 79^2) = √(12544 + 12544) = √25088 ≈ 158.39 units
The direction of R relative to due west is the angle θ found by tan(θ) = B/A. Since A and B have the same magnitude, θ = 45° south of west.
For vector A - B, we reverse vector B and again use the Pythagorean theorem to find the magnitude, which will be the same as for A + B. However, the direction will be 45° north of west since B is now pointing in the opposite direction to before. Therefore, vector A - B also has a magnitude of 158.39 units and is directed 45° north of west.