Answer
$\phi = 48.5^{\circ}$
Work Step by Step
In part (a), we found that $a \cdot b = 2.97$
In part (b), we found that $a \times b = 1.51\hat{i}+ 2.67\hat{j} - 1.36\hat{k}$
We can find the magnitude of $a \times b$:
$\sqrt{(1.51)^2+(2.67)^2+(-1.36)^2} = 3.36$
We can find the angle $\phi$ between the two vectors:
$\frac{a\times b}{a \cdot b} = \frac{3.36}{2.97}$
$\frac{ab~sin~\phi}{ab~cos~\phi} = \frac{3.36}{2.97}$
$tan~\phi = \frac{3.36}{2.97}$
$\phi = tan^{-1}~\frac{3.36}{2.97}$
$\phi = 48.5^{\circ}$
