Three-dimensional (3D) coordinate geometry is a branch of mathematics that studies geometric shapes and their relationships in three-dimensional space. It involves representing points, lines, planes, and other geometric objects using a coordinate system consisting of three perpendicular axes (x, y, and z) to specify their positions.

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In 3D coordinate geometry, points are represented as ordered triples (x, y, z), where each coordinate represents the distance along the corresponding axis. The origin (0, 0, 0) serves as the reference point for measuring distances.

Key concepts in 3D coordinate geometry include:

• Distance and Midpoint: Calculating the distance between two points in 3D space using the distance formula and finding the midpoint between two points.
• Equations of Lines: Representing lines using vector equations, parametric equations, or the symmetric form, as well as determining the direction and position of lines.
• Equations of Planes: Describing planes using different forms of equations, such as the general form, normal form, or intercept form, and understanding their orientations and intersections.
• Intersection of Lines and Planes: Analyzing the point(s) where lines and planes meet and finding their coordinates.

Vector Operations: Performing vector addition, subtraction, scalar multiplication, dot product, and cross product operations in 3D space.