Байарыст 2008 №5 вариант 7

Bayarystanov AO 2008 work №5 option 7
A₁ (5; 5; 4) with four points; А₂ (1; –1; 4); А₃ (3; 5; 1); А₄ (5; 8; –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.

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