Three Dimensional Geometry
Direction cosines of a line are the cosines of the angles made by the line with the positive direction of coordinate axes.
If l, m and n are direction cosines of the line, then l2 + m2 + n2 = 1.
Direction ratios of a line are the numbers that are proportional to the direction cosines of a line.
The direction ratios of the line joining A(x1, y1, z1) and B(x2, y2, z2) are
x2 – x1, y2 – y1, z2 – z1.
The equation of a line through a given point and parallel to a given vector can be given in both form vector and Cartesian.
Equation of a line passing through two given points can be given in both form vector and Cartesian.
Angle between two planes can be given in both form vector and Cartesian..
The shortest distance between two skew lines is the line segment perpendicular to both the lines and it can be calculated using the formula given in vector form or Cartesian form.
The angle between the two planes is defined as the angle between the normals to the plane.
The angle between a line and a plane is the complement angle between the line and the normal to the plane.
Keywords: Coplanar Lines, Direction cosines of a line, Direction ratios of a line, Intercepts, Magnitude, Normal to a plane, Plane, Position vector