x – x1 / a = y – y1 / b = z – z1 / c, it is also called the symmetrically form of a line.
Any point P on this line may be taken as( x1 + λa, y1 + λb, z1 + λc), where λ ∈ R is parameter.
If a, b, c are replaced by direction cosines 1, m, n, then λ, represents distance of the point P from the fixed point A.
2. Equation of a straight line joining two fixed points A( x1, y1, z1) and B( x2, y2, z2) is given by
x – x1 / x2 – x1 = y – y1 / y2 – y1 = z – z1 / z2 – z1
3. Vector equation of a line passing through a point with position vector a and parallel to vector b is r = a + λ b, where A, is a parameter.
4. Vector equation of a line passing through two given points having position vectors a and b is r = a + λ( b – a), where λ is a parameter.
5.( a) The length of the perpendicular from a point on the line r – a + λ b is given by
( b) The length of the perpendicular from a point P( x1, y1, z1) on the line
where, 1, m, n are direction cosines of the line.