Option 4 DHS 3.1
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DHS-3.1
№1.4. Given the four points A1 (2; 4; 3); A2 (1; 1; 5); A3 (4; 9; 3); A4 (3; 6; 7). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight A1A2. Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) cosine of the angle between the coordinate plane Oxu and the plane A1A2A3;
No. 2.4. Make an equation for a plane passing through point A (2; –3; 5) parallel to the Oxy plane.
No. 3.4. Prove that a straight line ...., is perpendicular to a straight line ..
№1.4. Given the four points A1 (2; 4; 3); A2 (1; 1; 5); A3 (4; 9; 3); A4 (3; 6; 7). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight A1A2. Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) cosine of the angle between the coordinate plane Oxu and the plane A1A2A3;
No. 2.4. Make an equation for a plane passing through point A (2; –3; 5) parallel to the Oxy plane.
No. 3.4. Prove that a straight line ...., is perpendicular to a straight line ..
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