Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

Find the equation of the plane passing through the point $D(1, 0, 2)$ and parallel to the $yz$-plane...

3D GeometryPlanesCoordinate Geometry
2025/6/28

The problem consists of two parts: (c) Given the position vectors of points $A(8, 4, -3)$, $B(6, 3, ...

Vectors3D GeometryArea of TriangleCross ProductVolume of ParallelepipedScalar Triple ProductDeterminants
2025/6/27

We are asked to find the area of a triangle with vertices (4,9), (2,1), and (-1,-7) using the determ...

AreaTriangleDeterminantsCoordinate Geometry
2025/6/27

The problem asks to find the equation of a line given two points in 3D space. The two points are $A(...

3D GeometryLinesParametric EquationsVectors
2025/6/27

The problem describes a composite object made of four identical rectangular plates. The question ask...

Center of GravityCenter of MassComposite ObjectsGeometric Shapes
2025/6/26

We are given three points $A(0,0,-1)$, $B(1,2,1)$, and $C(-2,-1,1)$ in a 3D space with an orthonorma...

3D GeometryVectorsDot ProductTrianglesEllipsesAnalytic GeometryConic Sections
2025/6/26

Given triangle $ABC$ with vertices $A(2, 6)$, $B(2+2\sqrt{2}, 0, 4)$, and $C(2+2\sqrt{2}, 4, 4)$. We...

3D GeometryDistance FormulaLaw of CosinesTrianglesIsosceles TriangleAngle Calculation
2025/6/24

Find the area of the triangle ABC, given the coordinates of the vertices A(2, 2, 6), B(2 + $2\sqrt{2...

3D GeometryVectorsCross ProductArea of Triangle
2025/6/24

In triangle $ABC$, we are given $AB=18$, $AC=12$, and $BC=15$. Point $D$ lies on $AB$ such that $BD=...

TriangleAreaSimilarityHeron's FormulaQuadrilateral
2025/6/23

The problem asks to find the value of angle $x$. We are given a triangle with two interior angles, ...

TrianglesAnglesExterior AnglesInterior Angles
2025/6/22