Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 853: 38

$\gamma=\frac{\pi}{3}$

Given: $\alpha= \frac{\pi}{4}$,$\beta= \frac{\pi}{3}$ Need to find $\gamma$ $cos ^2\alpha+ cos ^2\beta+ cos^2 \gamma=1$ $cos ^2(\frac{\pi}{4})+cos ^2(\frac{\pi}{3})+cos^2 \gamma=1$ $\frac{1}{2}+\frac{1}{4}+cos^2 \gamma=1$ $cos^2 \gamma=\frac{1}{4}$ $cos \gamma=\frac{1}{2}$ $\gamma=\frac{\pi}{3}$