Option 3 DHS 3.1

Option 3 DHS 3.1

DHS-3.1
№ 1.3. There are four points A1 (3; 5; 4); A2 (5; 8; 3); A3 (1; 2; –2); A4 (–1; 0; 2). 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;
№2.3. Find the distance from the point to the plane.
№3.3. Make a straight line equation; passing through point M (1; –3; 3) and forming angles with coordinate axes, respectively, 60; 45 and 120.