Ch 11 - Introduction to Three Dimensional Geometry11th Mathematics
Intersection of 3D Coordinate Axes
What is the geometric relationship and intersection property of the X, Y, and Z axes in three-dimensional space?
What is the geometric relationship and intersection property of the X, Y, and Z axes in three-dimensional space?
Geometric Relationship
- Point 1: The three coordinate axes (X, Y, and Z) intersect strictly at a single spatial point called the origin .
- Point 2: The axes are mutually perpendicular to each other in 3-dimensional space (each pair forms a rigorous angle).
Prism Memory Hook
A premium mnemonic for this topic is available in the Prism App.
3D Coordinate Planes
What are the three distinct coordinate planes in 3D geometry and how are they mathematically formed?
What are the three distinct coordinate planes in 3D geometry and how are they mathematically formed?
Formation of Coordinate Planes
- XY-Plane: Formed by the intersection and span of the X and Y axes.
- YZ-Plane: Formed by the intersection and span of the Y and Z axes.
- ZX-Plane: Formed by the intersection and span of the Z and X axes.
Prism Memory Hook
A premium mnemonic for this topic is available in the Prism App.
Locus Equations of Coordinate Axes
How do you mathematically represent the X, Y, and Z coordinate axes as locus equations in 3D space?
How do you mathematically represent the X, Y, and Z coordinate axes as locus equations in 3D space?
Locus Representations
- X-axis: Represented rigorously by the simultaneous intersection of planes AND .
- Y-axis: Represented rigorously by the simultaneous intersection of planes AND .
- Z-axis: Represented rigorously by the simultaneous intersection of planes AND .
Prism Memory Hook
A premium mnemonic for this topic is available in the Prism App.
Also in this chapter
32 more cards to study in Prism
- 4Locus Equations of Coordinate Planes
- 5Equation of Parallel Coordinate Planes
- 6Lines Parallel to Coordinate Axes
- 7Division of Space into Octants
- 8Octant Sign Convention Algorithm
- 9Coordinates of a Point strictly on the Axes
- 10Coordinates of a Point strictly on the Planes
- 11Foot of Perpendiculars: Axes vs. Planes
- 12Perpendicular Distance from Coordinate Planes
- 13Perpendicular Distance from Coordinate Axes
- 14Reflection / Image of a Point in 3D Planes
- 153D Distance Formula
- 16Distance from the Origin
- 17Longest Diagonal of a Rectangular Parallelepiped
- 18Extrapolating Cuboid Vertices from a Principal Diagonal
- 19Circumcenter of a Right Tetrahedron
- 20Collinearity Check (Distance Method)
- 21Proof SOP: Triangle Types in 3D
- 22Proof SOP: Parallelogram vs. Rectangle
- 23Proof SOP: Rhombus vs. Square
- 24Equidistant Point Locus (Setup Phase)
- 25Equidistant Point Locus (Expansion Phase)
- 26Double Radical Locus (Trap Avoidance)
- 27Double Radical Locus (Expansion Phase)
- 28Internal Section Formula
- 29External Section Formula
- 30Fractional Division Trap (p/q of the way)
- 31Mid-Point Formula
- 32Centroid of a Triangle in 3D
- 33Plane Intersection Ratio (k:1 Method)
- 34Collinearity Check (Section Formula Method)
- 35Internal Angle Bisector Theorem (3D Coordinates)
Premium Chapter
11th Mathematics
The remaining 32 cards of Ch 11 - Introduction to Three Dimensional Geometry are available in the Aspira Prism App with full interactive study tools, spaced repetition, and memory hooks.
Get Started with Prism