IDZ Ryabushko 3.1 Variant 22

№1 Given four points A1 (4; 2; 10); A2 (1; 2; 0); A3 (3; 5; 7); A4 (2; –3; 5). Draw up the equations: a) plane A1A2A3; b) straight line A1A2; c) direct A4M; perpendicular to the glossiness A1A2A3; d) direct A3N; parallel line A1A2; e) the 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 Make an equation for the plane passing through the point M (2; 3; –1) and the line x = t – 3; y = 2t + 5; z = –3t + 1.

№3 Find the point of intersection of the line (x-7) / 5 = (y-1) / 1 = (z-5) / 4 and the plane 3x – y + 2z – 8 = 0.