Question

найти угол плоскости x+2y+2z-3=0, 2x-y+2z+5=0

Answer 1

$alpha :; ; x+2y+2z-3=0; ; to; ; vec {n_1}=(1,2,2)\\ beta :; ; 2x-y+2z+5=0; ; to ; ; vec{n_2}=(2,-1,2)\\cos( alpha widehat {, }beta )= frac{vec{n_1}cdot vec {n_2}}{|vec{n_1}|cdot |vec {n_2}|} = frac{2-2+4}{sqrt{1+4+4}cdot sqrt{4+1+4}} = frac{4}{3cdot 3} =frac{4}{9}\\( alpha widehat {, }beta )=arccos , frac{4}{9}$