Equation of a line through a point and having direction cosines l, m, n is

Equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is given by :

Vector equation of a line that passes through two points whose position vectors are is given by:

Cartesian equation of a line that passes through two points and is

Cartesian equation of a line that passes through two points and is given by : .

If is the acute angle between , then

If is the acute angle between , then cosine of the angle between these two lines is given by :

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

Shortest distance between

is given by :

Shortest distance between the lines and is

Shortest distance between the lines and is given by:

If a line makes angles with the x, y and z – axes respectively, find its direction cosines.

If a line makes angles with the x, y and z – axes respectively, then the direction cosines of this line is given by :

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector.

The equation of the line which passes through the point (1, 2, 3) and is parallel to the vector

, let vector and vector ,

the equation of line is :

.