IDZ Ryabushko 3.1 Option 17

No. 1 Given four points A1(6;6;5); A2(4;9;5); A3(4;6;11); A4(6;9;3). Make up the equations: a) plane A1A2A3; b) straight A1A2; c) straight line A4M, perpendicular to the plane A1A2A3; d) straight line A3N parallel to straight line A1A2; e) a plane passing through point A4, perpendicular to straight line A1A2. Calculate: e) the sine of the angle between straight line A1A4 and plane A1A2A3; g) cosine of the angle between the coordinate plane Oxy and the plane A1A2A3; No. 2 Create an equation for a plane passing through the point M(1;–1;2) perpendicular to the segment M1M2; if M1(2;3; –4); M2(–1;2; –3 ). No. 3 Show that the line is parallel to the plane x + 3y – 2z + 1 = 0; and straight line x = t + 7; y = t – 2; z = 2t + 1 lies in this plane.

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