Practice Test 1

In an $xy$-coordinate system where directions are measured in degrees from the positive $x$-axis, vector $\mathbf{u}$ has magnitude $10$ at direction $30^\circ$, and vector $\mathbf{v}$ has magnitude $10$ at direction $150^\circ$. For the vectors described, what is the magnitude of $\mathbf{u}+\mathbf{v}$ (magnitude only)?

A hiker walks $6$ km due east (direction $0^\circ$ from the positive $x$-axis), then walks $8$ km due north (direction $90^\circ$). Using the information provided, what are the magnitude and direction of the hiker’s resultant displacement (direction as an angle from the positive $x$-axis)?