Bayarystanov 2018-1 №6 option 5

Bayarystanov A.O. 2018-1 work No. 6 option 5
Four points are given A₁(4;5;1); A₂(7;3;-1); A₃(2;1;-2); A₄(–1;3;7). 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.