Chapter 11 - Section 11.3 - The Dot Product - Exercises - Page 616: 10

$0.84$ rad

The formula to calculate the angle between two planes is: $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})$ Here, $p=\lt 2,-2,1 \gt$ and $q=\lt 3,0,4 \gt$ $|p|=\sqrt{2^2+(-2)^2+1^2}= \sqrt {9}=3$ and $|q|=\sqrt{3^2+0^2+(4)^2}=\sqrt {25}=5$ Thus, $ \theta = \cos ^{-1} (\dfrac{p \cdot q}{|p||q|})=\cos ^{-1} \dfrac{10}{ (3)(5)})=\cos ^{-1} \dfrac{10}{15}$ or, $ \theta \approx 0.84$ rad