Consider two planes with Cartesian equations,
![\[ x + y = 1, \qquad y + z = 2. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-c71036cf797af6ff7e08a8560023b7ab_l3.png "Rendered by QuickLaTeX.com")
Determine the angle between the planes.
For the two planes we have normals 
and 
. Therefore, the angle between the planes is
![\[ \cos \theta = \frac{N_1 \cdot N_2}{\lVert N_1 \rVert \lVert N_2 \rVert} = \frac{1}{2} \qquad \implies \qquad \theta = \frac{\pi}{3} \ \text{or} \ \frac{2 \pi}{3}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-7af78b309961fb72ac39606e8ef8f716_l3.png "Rendered by QuickLaTeX.com")
Consider two planes with Cartesian equations,
Determine the angle between the planes.
For the two planes we have normals and . Therefore, the angle between the planes is