IDZ Ryabushko 3.1 Variant 24
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No. 1 Given four points A1 (5; 3; 7); A2 (–2; 3; 5); A3 (4; 2; 10); A4 (1; 2; 7). Draw up the equations: a) plane A1A2A3; b) straight line A1A2; c) direct A4M; perpendicular to the plane A1A2A3; d) direct A3N; parallel line A1A2; e) a plane passing through point A4; perpendicular to the straight 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 Determine at what value B the planes x - 4y + z - 1 = 0 and 2x + By + 10z - 3 = 0 will be perpendicular.
№3 Draw up the general equation of the line formed by the intersection of the plane x + 2y - z + 5 = 0 with the plane passing through the axis Oy and point M (5; 3; 2).
№2 Determine at what value B the planes x - 4y + z - 1 = 0 and 2x + By + 10z - 3 = 0 will be perpendicular.
№3 Draw up the general equation of the line formed by the intersection of the plane x + 2y - z + 5 = 0 with the plane passing through the axis Oy and point M (5; 3; 2).
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