Question

what is the angle in radians between the vectors?

a = (-9, 8, -5) and
b = (2, 9, -9)?

Answer 1

\[\vec a\cdot\vec b=\|\vec a\|\|\vec b\|\cos\theta\implies\theta=\cos^{-1}{\vec a\cdot\vec b\over\|\vec a\|\|\vec b\|}\]

Answer 2

A nice Mathematica function, VectorAngle, can calculate the answer.\[\text{VectorAngle}[\{-9,8,-5\},\{2,9,-9\}] = \text{ArcCos}\left[\frac{99}{2 \sqrt{7055}}\right]=53.8907{}^{\circ} \]