IDZ Ryabushko 3.1 Variant 29
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№1 Given four points A1 (2; –1; 7); A2 (6; 3; 1); A3 (3; 2; 8); A4 (2; –3; 7). Draw up the equations: a) plane A1A2A3; b) straight line A1A2; c) a straight line A4M perpendicular to the plane A1A2A3; d) line A3N parallel to line A1A2; d) a plane passing through point A4, perpendicular to the line A1A2. Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) the cosine of the angle between the Ohu coordinate plane and the A1A2A3 plane.
№2 Make an equation for the plane passing through the points M (2; 3; –5); N (–1; 1; –6); parallel to the vector a = (4; 4; 3).
№3 Draw up the canonical equation of the line passing through the point M (1; –5; 3) perpendicular to the lines ... and x = 3t + 1; y = –t – 5; z = 2t + 3.
№2 Make an equation for the plane passing through the points M (2; 3; –5); N (–1; 1; –6); parallel to the vector a = (4; 4; 3).
№3 Draw up the canonical equation of the line passing through the point M (1; –5; 3) perpendicular to the lines ... and x = 3t + 1; y = –t – 5; z = 2t + 3.
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