Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to find the unit vectors perpendicular to the plane determined by the three poin...
Vectors3D GeometryCross ProductUnit VectorsPlanes
2025/6/2
Find all vectors that are perpendicular to both vectors $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ an...
VectorsCross Product3D GeometryLinear Algebra
2025/6/2
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