## Toppers Notes on 3-D Geometry

Below you will get an embedded PDF file of the topic “toppers notes on 3-D Geometry for jee main & Advanced”, where you have the facility to read, download, or print the document at your convenience. You can take the help of these short notes for the preparation of All India engineering examinations like JEE Main & JEE Advanced. In fact, these notes are helpful to crack any entrance exam in which the mathematics up to 12th class is asked.

### Table of Content

• Coordinates of a point in space (Cartesian coordinates, Cylindrical coordinates, Spherical Polar coordinates).
• Distance Formula, Section Formula, Centroid of a triangle, Centroid of a tetrahedron.
• Condition of collinearity, Volume of a tetrahedron.
• Direction cosines, Direction ratios.
• Projection of a vector on a line segment.
• Equation of a plane.
• Equation of system of planes.
• The angle between two planes.
• Parallelism and perpendicularity of planes.
• Two sides of a plane.
• Length of the perpendicular from a point to the plane.
• distance between two perpendicular planes.
• Equation of angle bisectors of two planes.
• Equation of a straight line in vector form and cartesian form.
• Changing the unsymmetrical form of a straight line into the symmetrical form.
• The angle between two straight lines.
• The equation of a straight line parallels to the given straight line.
• Equation of straight line perpendicular to a given straight line.
• Condition whether that two straight lines will intersect each other or not.
• The foot of the perpendicular from a point to a straight line.
• The shortest distance between two skew lines.
• Image of a point with respect to a plane.
• The angle between a straight line and a plane.
• Equation of a sphere.
• Section of a sphere.
• The intersection of a straight line and a sphere.
• The angle of intersection between the two is a sphere.