Bayarystanov 2008 №5 option 6

Bayarystanov AO 2008 work №5 option 6
A₁ (0; 7; 1) with four points; А₂ (2; –1; 5); А₃ (1; 6; 3); А₄ (3; –9; 8). 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.