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In this video I go over equations of lines and planes in 3D coordinates. This section is part of my calculus book chapter titled Vectors and the Geometry of Space. In 2D coordinates, a line can be described by a point on the line and its slope or direction. Similarly, a line in 3D coordinates can be described by a point on the line and a vector parallel to it which thus serves as the direction. A plane in 3D coordinates is described by a point on the plane and a vector perpendicular to the plane. The plane equation utilizes the fact that the dot product of two perpendicular vectors is equal to zero. Furthermore, the cross product is also used in determining the perpendicular vector, termed a normal vector. I go through several related concepts, such as scalar and vector equations of lines, segments of lines, and linear equations of planes, as well as many examples to give a thorough examination of 3D lines and planes.
The topics covered as well as their timestamps are listed below.
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Discovery Project: The Geometry of a Tetrahedron: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
The Cross Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
The Dot Product: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
Complex Numbers as Rotation Matrices: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
Vectors: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
3D Coordinate Systems: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems .
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