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

Vectors and Three-Dimensional Geometry

Mathematics

Vector algebra, lines and planes in space, and the coordinate geometry of three dimensions.

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72 problems
Exam:
Type:
1.
A drone takes off from a launch pad at the origin… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
2.
A tow rope pulls a barge with the force F = 2 i - 3 j + 6 k kilonewtons… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
3.
A survey laser is aimed from the origin of a coordinate system with the z-axis pointing up… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
4.
A boat leaves one bank of a river and heads straight across, due north, at 4 m/s relative to the… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
5.
Two cables pull on a fixed hook on a crane… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
6.
The figure of a garden tile is a regular hexagon ABCDEF with a side of 2 centimetres… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
7.
A cable runs from the top of one mast at A(1, 2, 3) to the top of another mast at B(7, 5, 12), with… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
8.
A site engineer lowers a straight cable into a pit… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
9.
Three radio masts stand at A(1, -2, 3), B(4, 1, 9) and C(k, 7, p), with lengths in kilometres… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
10.
In the triangle ABC, take A as the origin, and write b = overrightarrowAB and c = overrightarrowAC… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Advanced
11.
Two steel rods are welded at a joint. Treat them as the vectors a and b drawn from the joint… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
12.
A surveyor records two displacement vectors a and b with lvert arvert = 3 metres and lvert brvert =… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
13.
Two cables pull on a ring with forces represented by the vectors a and b… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
14.
A sail is cut in the shape of the triangle with corners A(1, 1, 1), B(2, 3, 3) and C(3, 2, -1)… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
15.
A cube-shaped storeroom has edges of 4 metres… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
16.
In a model of a frame, three bars point along the vectors a = 2 i + j + 3 k, b = i + j + k and c =… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
17.
Three ropes of the same strength pull on a ring, and the ring stays at rest… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
18.
A constant force F = 5 i - 2 j + 4 k newtons moves a small trolley through the displacement d = 3 i… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
19.
A pipeline runs in the direction b = i + 2 j + 2 k… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
20.
A lighthouse stands at the origin of a map, with distances in kilometres… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Advanced
21.
A wrench is on a bolt at the origin of a coordinate system, with the bolt along the y-axis… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Easy
22.
Two struts of a frame point along the vectors a = i + 2 j + 2 k and b = 2 i - 2 j + k… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
23.
Three forces in a plane keep a ring at rest, so their vectors add up to zero… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Hard
24.
A triangular plot of land has its corners at A(1, 1, 1), B(3, 3, 2) and C(2, -1, 3), with… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
25.
Two vectors a and b have the sizes 3 and 5, and their dot product is 9… New
High School (11–12) · Vectors and Three-Dimensional GeometryStemPy LabStemPy Lab
Medium
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