Chapter 11, Problem 32P

Vector $\stackrel{\to }{A}$ points 30° counterclockwise from the x-axis. Vector $\stackrel{\to }{B}$ has twice the magnitude of $\stackrel{\to }{A}$. Their product $\stackrel{\to }{A}\times \stackrel{\to }{B}$ has magnitude A² and points in the negative z-direction. What’s the direction of vector $\stackrel{\to }{B}$?