Bayarystanov 2018-1 №6 option 4

Bayarystanov AO 2018-1 work №6 options 4
A₁ (0; 5; –3) with four points; А₂ (2; 1; 5); А₃ (3; 4; 1); А₄ (5; –2; 3). It is necessary to find: a) the equation of the plane А₁А₂А₃; b) the equation of the salt AAA; c) the equation of the salt A₄M perpendicular to the plane A₁A₂A₃; d) the equation of the salt A₄N, which is parallel to the salt A₁A₂; e) Calculate the sine of the angle between the plane А₁А₂А₃ and the salt А₁А₄; e) Calculate the cosine of the angle between the axis coordinate plane and the plane А₁А₂А₃.