Reshebnik Ryabushko. Solved IDZ 3.1, Option 10
Replenishment date: 20.06.2020
Content: 10v-IDZ3.1.rar (38.23 KB)
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Description
1. Given four points A1 (x1, y1, z1), A2 (x2, y2, z2), A3 (x3, y3, z3), A4 (x4, y4, z4)
Make 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:
f) sine of the angle between straight line A1A4 and plane A1A2A3;
g) cosine of the angle between the Oxy coordinate plane and the A1A2A3 plane;
1.10 A1 (6, 8, 2), A2 (5, 4, 7), A3 (2, 4, 7), A4 (7, 3, 7)
2. Solve the following tasks
2.10 Make an equation of the plane in "segments" if it passes through the point M (6, −10, 1) and cuts off the segment a = −3 on the Ox axis, and the segment c = 2 on the Oz axis
3. Solve the following tasks
3.10 At what value of A is the plane Ax + 3y - 5z + 1 = 0 parallel to the straight line (x-1) / 4 = (y + 2) / 3 = z / 1?
Make 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:
f) sine of the angle between straight line A1A4 and plane A1A2A3;
g) cosine of the angle between the Oxy coordinate plane and the A1A2A3 plane;
1.10 A1 (6, 8, 2), A2 (5, 4, 7), A3 (2, 4, 7), A4 (7, 3, 7)
2. Solve the following tasks
2.10 Make an equation of the plane in "segments" if it passes through the point M (6, −10, 1) and cuts off the segment a = −3 on the Ox axis, and the segment c = 2 on the Oz axis
3. Solve the following tasks
3.10 At what value of A is the plane Ax + 3y - 5z + 1 = 0 parallel to the straight line (x-1) / 4 = (y + 2) / 3 = z / 1?
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.