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  1. Problems
  2. /Vectors and Three-Dimensional Geometry
  3. /Three-Dimensional Geometry

Three-Dimensional Geometry

Mathematics
+ Upload a Problem
More in Vectors and Three-Dimensional GeometryIntroduction to Three-Dimensional GeometryVector AlgebraThree-Dimensional Geometry
30 problems
Exam:
Type:
1.
A slab is cut along the plane 2x - y + 2z = 3, with coordinates in metres… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
2.
Two walls of a tunnel lie in the planes 2x + y - z = 3 and x + 3y + 2z = 9, with coordinates in… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
3.
Two flat plates are parallel, and they lie in the planes 2x - 2y + z = 8 and 2x - 2y + z = -4, with… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
4.
A ceiling in a hall is tilted and lies in the plane 4x - 4y + 7z = 7, with coordinates in metres… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
5.
A straight pipe is to run above a flat roof without touching it… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
6.
A straight cable passes through the point A(1, 2, 0) with direction ratios (4, -3, 12), with… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
7.
Two sloping roofs of a hall lie in the planes 2x - y + 2z = 5 and x - 4y + 8z = 3, with coordinates… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
8.
A glass panel for a roof lies in a plane that meets the three coordinate axes at the points A, B… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
9.
A surveyor marks three points on a flat piece of ground, in metres: A(1, 0, 2), B(2, 1, 0) and C(0… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
10.
A flat roof panel passes through the point A(2, -1, 4), with coordinates in metres, and a… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
11.
A radio mast stands at P(9, -3, 9), with coordinates in metres… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
12.
A power line passes through the point (1, -2, 0) with direction ratios (3, 4, 12), with lengths in… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
13.
A straight cable runs along the line through A(0, 1, 2) with direction ratios (2, 2, 1)… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
14.
Two straight pipes in a chemical plant pass without touching… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
15.
Two supports in a stadium roof lie along the lines (x + 2)/2 = (y - 3)/3 = (z - 4)/6 and x/3 = (y… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
16.
Two parallel cables run along the lines r = (î + ĵ + k̂) + λ(î + 2ĵ + 2k̂) and r = (3î - 7ĵ - k̂) +… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
17.
Two cables follow the lines r = (2î - ĵ + k̂) + λ(î + 2ĵ + 2k̂) and r = (-î + 2ĵ + k̂) + µ(î + ĵ)… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
18.
Two drones fly along straight paths over a wide field… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
19.
Two pipes in a plant room follow the lines x/1 = (y - 1)/2 = (z + 1)/3 and (x - 1)/1 = (y - 3)/k =… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
20.
Two straight tunnels are being dug in a mine, and a surveyor must know whether they will break into… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
21.
A storage box is 4 metres long, 3 metres wide and 12 metres tall… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
22.
Two struts of a roof truss lie along lines with direction ratios (k, 2, -3) and (1, k, 4)… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
23.
Two cables hang in a stadium. The first has direction ratios (2, 3, 6) and the second has direction… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
24.
An air traffic controller tracks an aircraft on its final descent… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
25.
Inside a warehouse a conveyor cable follows the line (x - 1)/3 = (y + 2)/0 = (z - 4)/(-2)… New
High School (11–12) · Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
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