Page 2 - XII(3-D)\3D(XII)L.N

 The vector equation of a line which passes through two points whose

position vectors are
 Cartesian equation of a line that passes through two
points (x 1,y 1,z 1) and (x 2,y 2,z 2) is

 If is the acute angle between and then,
Cos =

 If are the equations of two lines, then the acute angle between the two
lines is given by

 Shortest distance between two skew lines is the line segment
perpendicular to both the lines.

 Shortest distance between two lines & in vector
form is

S.D=

 Shortest distance between the line &

 Distance between parallel lines &

=

 In the vector form, equation of a plane which is at a distance d from
the origin ,and is the unit vector normal to the plane through the

origin is
 Equation of a plane which is at a distance of d from the origin and the
direction cosines of the normal to the plane as l, m, n is
.