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 .