Bayarystanov 2018-1 №6 option 3

Bayarystanov AO 2018-1 work №6 options 3
A₁ (2; –4; 3) with four points; А₂ (5; 2; 1); А₃ (0; 5; 2); А₄ (1; –2; –1). 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 А₁А₂А₃; 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.