3.3.27 Line and plane in space
condition: Given planes \( \quad \alpha: 2 x-y+3 z-1=0 \), \( \beta: x+2 y+z=0 \). Find: a) the angle between the planes \( \alpha \) and \( \beta \); b) coordinates of at least one vector parallel (at the same time) to the planes \( \alpha \) and \( \beta \) c) create an equation of a plane perpendicular to the planes \( \alpha, \beta \) and passing through the origin.
Straight lines and planes in space. Intersection of lines and planes, calculation of the distance of a line and a plane, angles between lines and planes, finding equations of lines and planes in space, and much more.