Final answer:
The questions involve proving the commutative property of vector addition and subtraction through practical examples of walking in different directions, and calculating the resulting displacement using vector components and trigonometry.
Step-by-step explanation:
The student's questions involve solving vector addition problems in a two-dimensional plane. These problems are designed to illustrate the commutative property of vector addition and subtraction, which states that the order in which vectors are added or subtracted does not affect the resultant vector. To prove this, vectors are described by their magnitude and direction relative to the cardinal directions (North, East, South, West).
In problem 6, the student first walks leg B (20.0 m, 40° south of west) and then leg A (12.0 m, 20° west of north). Following the order of B + A, we expect the same result as if the order were reversed (A + B), demonstrating the commutative property A + B = B + A.
For problems 7a and 7b, the student is tasked to subtract one vector from another and show that R'' = B - A = -R'. The calculations involve breaking the vectors into their horizontal (east-west) and vertical (north-south) components, adding or subtracting these components, and then using trigonometry to find the final resultant vector's magnitude and direction.