# 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 (x1, y1, z1) and having direction ratios a, b, c is (parameter).

Any point on the line is (x1 + λa, y1 + λb, z1 + 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 (x1, y1, z1) and (x2, y2, z2) is

Notes:
• Two straight lines in a space which are neither parallel nor intersecting are called skew-lines.

Thus, the skew-lines are those lines which do not lie in the same plane.

For lines  and  or lines

and

where ,

• 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 (x1 + , y1 + , z1 + ), where λ = .