Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
We are given two points A and B with coordinates A(3, 2) and B(5, 6). We need to find the column vec...
VectorsCoordinate GeometryVector Operations
2025/4/9
The problem states that Noah has 50 meters of fencing to enclose a rectangular garden. We need to dr...
PerimeterRectanglesAlgebraic Equations
2025/4/9
ABCD is a parallelogram and AX is parallel to CY. We need to prove: (i) $\angle AXB = \angle CYD$ (i...
ParallelogramsCongruenceAnglesParallel LinesTriangles
2025/4/9
The problem describes a piece of land consisting of a rectangle and a semi-circle. We need to find: ...
PerimeterAreaRectangleSemi-circleRatioTriangle
2025/4/9
The problem asks us to find the volume of a parallelepiped defined by three edge vectors. The edge v...
3D GeometryVectorsParallelepipedScalar Triple ProductDeterminantsVolume
2025/4/9
We need to find the equation of a plane that passes through the point $(-1, -2, 3)$ and is perpendic...
Plane EquationsVectorsCross Product3D Geometry
2025/4/9
We need to find the unit vectors perpendicular to the plane determined by the points $(1, 3, 5)$, $(...
Vectors3D GeometryCross ProductUnit VectorsPlanes
2025/4/9
Find all vectors that are perpendicular to both vectors $a = i + 2j + 3k$ and $b = -2i + 2j - 4k$.
VectorsCross ProductLinear Algebra3D GeometryPerpendicular Vectors
2025/4/9
Given vectors $a = (3, 3, 1)$, $b = (-2, -1, 0)$, and $c = (-2, -3, -1)$, we need to find the follow...
VectorsCross ProductDot ProductVector Algebra
2025/4/9
Given three vectors $a = (3, 3, 1)$, $b = (-2, -1, 0)$, and $c = (-2, -3, -1)$, we are asked to find...
VectorsCross ProductDot ProductVector Algebra
2025/4/9