determine the angle between the planes 2x + 2y + 7z = 8 and 3x - 4y + 4z = 5

Answer 1

let Ø be the angle between their normals

(2,2,7)∘(3,-4,4) = √57√41cosØ
cosØ = (6 - 8 + 28)/(√57√41)
Ø = appr. 57.5°

so the two planes form an angle of 180-57.5 or 122.5°