$($similar to pb $\mathrm{.}55$ section $13\mathrm{.}1,$ textbook$)$ Determine the necessary air speed and heading that a pilot must maintain in order to fly her commercial jet west at a speed of $480m\frac{i}{h}r$ relative to the ground in a crosswind that is blowing $60$ south of east at $20m\frac{i}{h}r.$

Use vectors and dot product to determine, to the nearest degree, the acute angle formed by two diagonals of a cube. Does the size of the cube matter? Briefly explain.