Chapter 5 - Inner Product Spaces - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 236: 69

orthogonal. $u\cdot v=0$.

The vectors ${u}=(\cos \theta, \sin \theta,-1), \quad {v}=(\sin \theta,-\cos \theta, 0)$ are orthogonal. Since $$u\cdot v=\cos \theta \sin \theta -\cos \theta \sin \theta+0=0,$$ then the angle between $u$ and $v$ is $\frac{\pi}{2}$.