Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to find the projection of vector $\textbf{w}$ onto vector $\textbf{u}$, given $\...
VectorsProjectionDot ProductLinear Algebra
2025/6/2
The problem asks us to find all vectors that are perpendicular to both $v = (1, -2, -3)$ and $w = (-...
VectorsDot ProductOrthogonalityLinear Algebra3D Geometry
2025/6/2
We are given three vectors: $a = (\sqrt{3}/3, \sqrt{3}/3, \sqrt{3}/3)$, $b = (1, -1, 0)$, and $c = (...
VectorsDot ProductAngles3D Geometry
2025/6/2
We are given two problems. Problem 43: An object's position $P$ changes so that its distance from $(...
3D GeometrySpheresPlanesDistance FormulaCompleting the Square
2025/6/2
The problem asks us to find the center and radius of the sphere given by the equation $4x^2 + 4y^2 +...
3D GeometrySphereCompleting the SquareEquation of a Sphere
2025/6/2
The problem asks us to identify the type of curve represented by the polar equation $r = \frac{4}{1 ...
Conic SectionsPolar CoordinatesHyperbolaEccentricity
2025/6/1
The problem asks us to identify the curve represented by the polar equation $r = \frac{-4}{\cos \the...
Polar CoordinatesConic SectionsEccentricityCoordinate Transformation
2025/6/1
We are asked to find the Cartesian equation of the graph of the polar equation $r - 5\cos\theta = 0$...
Polar CoordinatesCartesian CoordinatesCoordinate GeometryCirclesEquation Conversion
2025/6/1
We are given several Cartesian equations and asked to find their corresponding polar equations. Prob...
Coordinate GeometryPolar CoordinatesEquation Conversion
2025/6/1
The problem is to eliminate the cross-product term in the equation $4xy - 3y^2 = 64$ by a suitable r...
Conic SectionsRotation of AxesHyperbolaCoordinate Geometry
2025/6/1