Bayarystanov 2018-1 №6 option 12

Bayarystanov A.O. 2018-1 work No. 6 option 11
Four points are given A₁(-5;1;-9); A₂(5;7;2); A₃(8;4;7); A₄(-3;-7;-1). It is necessary to find: a) the equation of the A₁A₂A₃ plane; b) equation of structure of A₁A₂; c) the equation of the structure A₄M perpendicular to the A₁A₂A₃ plane; d) equation of A₄N structure parallel to A₁A₂ structure; e) calculate the sine of the angle between the A₁A₂A₃ plane and the A₁A₄ structure; f) Calculate the cosine of the angle between the axis coordinate plane and the A₁А₂A₃ plane.