Bayarystanov 2008 №5 option 1

Bayarystanov AO 2008 work №5 option 1
A₁ (3; 1; 4) with four points; А₂ (–1; 6; 1); А₃ (-1; 1; 6); А₄ (0; 4; -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.