Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
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
We are given three vectors, $a = -3i + 2j - 2k$, $b = -i + 2j - 4k$, and $c = 7i + 3j - 4k$. We need...
VectorsCross ProductDot Product3D Geometry
2025/4/9
We are given a circle with points A, B, Q, and R on its circumference. PQ and RS are tangents to the...
Circle GeometryCyclic QuadrilateralTangentsAnglesAlternate Segment TheoremRectangle
2025/4/9
The problem asks for an example of an equation of a line with zero slope. A line with zero slope is ...
Linear EquationsSlopeHorizontal Lines
2025/4/9
ABCD is a circle with center O. $\angle AOB = 80^{\circ}$ and $AB = BC$. We need to calculate (i) $\...
CirclesAnglesCyclic QuadrilateralsIsosceles Triangles
2025/4/8
The problem consists of two parts. Part (a) asks to find the measures of angle $Q\hat{A}B$ and angl...
CirclesAnglesTangentsCyclic QuadrilateralsIsosceles TrapezoidGeometric Proofs
2025/4/8