Chapter 1.10, Problem 1.10TYU

Vector $\stackrel{\to }{A}$ has magnitude 2 and vector $\stackrel{\to }{B}$ has magnitude 3. The angle ϕ between $\stackrel{\to }{A}$ and $\stackrel{\to }{B}$ is (i) 0°, (ii) 90°, or (iii) 180°. For each of the following situations, state what the value of ϕ must be. (In each situation there may be more than one correct answer.) (a) $\stackrel{\to }{A}\cdot \stackrel{\to }{B}=0$; (b) $\stackrel{\to }{A}\times \stackrel{\to }{B}=0$; (c) $\stackrel{\to }{A}\cdot \stackrel{\to }{B}=6$; (d) $\stackrel{\to }{A}\cdot \stackrel{\to }{B}=-6$; (e) (magnitude of $\stackrel{\to }{A}\times \stackrel{\to }{B}$) = 6.