# Straight line passing through a point and parallel to given vector

**Vector form**A line passing through point and parallel to , where

*λ*is parameter (scalar) where = position vector of any point on the line.

**Cartesian form**Equation of line passing through the point (

*x*

_{1},

*y*

_{1},

*z*

_{1}) and having direction ratios

*a*,

*b*,

*c*is (parameter).

Any point on the line is (

*x*_{1}+*λa*,*y*_{1}+*λb*,*z*_{1}+*λc*)# Line passing through two given points

**Vector form**The vector equation of a line passing through two points whose position vectors is

**Cartesian form**Equation of straight line passing through (

*x*

_{1},

*y*

_{1},

*z*

_{1}) and (

*x*

_{2},

*y*

_{2},

*z*

_{2}) is

*Notes:*- Two straight lines in a space which are neither parallel nor intersecting are called skew-lines.
- Angle between the lines is cos
^{–1} - Lines are parallel if , where
*t*is scalar. - Lines are perpendicular if = 0.
- Lines are coplanar if = 0
- Shortest distance between the lines is .

# Foot of perpendicular from point on the line

Let “

*L*” be the foot of perpendicular drawn from*P*(*α*,*β*,*γ*) on the line; is (*x*_{1}+*aλ*,*y*_{1}+*bλ*,*z*_{1}+*cλ*), where*λ*= .