ANALYTICAL GEOMETRY IN SPACE: VARIOUS EXERCISES ON LINES AND PLANES
Analytic Geometry in Space: Exercises on Points, Lines, and Planes
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Equations of a Line and a Plane Exercises on the equations of a line and their different types (vector, parametric, continuous, and general or implicit), enabling students to obtain points and direction vectors from the equation and to write the equation from given data. Exercises on the equations of a plane and their different types (vector, parametric, and general or implicit), enabling students to obtain points, direction vectors, and normal or associated vectors from the equation and to write the equation from given data.
Coordinate axes and planes. Exercises on understanding coordinate axes (their equations as lines, points, direction vectors, etc.) and coordinate planes (their equations as planes, points, direction vectors, etc.).
Projections and the symmetric point. Exercises on projecting a point onto a line or plane. Projecting a line onto a plane. Finding the symmetric point of a point with respect to another point, line, or plane.
Relative positions. Exercises on studying the relative position between planes, planes, lines, and three... Planes.
Distances. Exercises on calculating the distance between two points, a point and a line, a point and a plane, two lines, a line and a plane, and two planes.
Common perpendicular line. Classic exercise on finding the line that intersects two other lines perpendicularly, the so-called common perpendicular.
Angles. Exercises on the angle formed by two lines, two planes, and a line and a plane.
Area of parallelogram ABCD and triangle ABC. Exercises on the area of a parallelogram and a triangle.
Volume of a parallelepiped and a tetrahedron. Exercises on calculating the volume of a parallelepiped and a tetrahedron.
Physicle of planes of a line. Exercises using the pencil of planes of a line as the intersection of two planes.