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

Vector Algebra

Mathematics
+ Upload a Problem
More in Vectors and Three-Dimensional GeometryIntroduction to Three-Dimensional GeometryVector AlgebraThree-Dimensional Geometry
30 problems
Exam:
Type:
1.
A parallelepiped has the edges a = i + j, b = j + k and c = i + 4 k, in metres… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Advanced
2.
A tent is a tetrahedron with the corners P(1, 0, 0), Q(0, 2, 0), R(0, 0, 3) and S(1, 1, 1), with… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
3.
Four joints of a steel frame have the coordinates A(1, 2, 3), B(2, 4, 5), C(0, 1, 1) and D(2, 2… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
4.
A concrete block leans to one side. Its three edges from one corner are a = 3 i + j - k, b = i + 2… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
5.
A parallelogram frame has its two diagonals along the vectors d₁ = 3 i + j - 2 k and d₂ = i - 3 j +… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
6.
Two vectors a and b have the sizes 3 and 5, and their dot product is 9… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
7.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
8.
Three forces in a plane keep a ring at rest, so their vectors add up to zero… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
9.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
10.
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) · Vector AlgebraA-LevelIBA-LevelIBStemPy LabStemPy Lab
Easy
11.
A lighthouse stands at the origin of a map, with distances in kilometres… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Advanced
12.
A pipeline runs in the direction b = i + 2 j + 2 k… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
13.
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) · Vector AlgebraA-LevelIBA-LevelIBStemPy LabStemPy Lab
Easy
14.
Three ropes of the same strength pull on a ring, and the ring stays at rest… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
15.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
16.
A cube-shaped storeroom has edges of 4 metres… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
17.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
18.
Two cables pull on a ring with forces represented by the vectors a and b… New
High School (11–12) · Vector AlgebraJEE MainA-LevelIB+24A-LevelIBStemPy LabStemPy Lab
Hard
19.
A surveyor records two displacement vectors a and b with lvert arvert = 3 metres and lvert brvert =… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
20.
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) · Vector AlgebraA-LevelIBA-LevelIBStemPy LabStemPy Lab
Easy
21.
In the triangle ABC, take A as the origin, and write b = overrightarrowAB and c = overrightarrowAC… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+23A-LevelIBStemPy LabStemPy Lab
Advanced
22.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+23A-LevelIBStemPy LabStemPy Lab
Hard
23.
A site engineer lowers a straight cable into a pit… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+23A-LevelIBStemPy LabStemPy Lab
Hard
24.
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) · Vector AlgebraA-LevelIBAEEE (Amrita)+19A-LevelIBStemPy LabStemPy Lab
Medium
25.
The figure of a garden tile is a regular hexagon ABCDEF with a side of 2 centimetres… New
High School (11–12) · Vector AlgebraA-LevelIBAEEE (Amrita)+23A-LevelIBStemPy LabStemPy Lab
Hard
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