Find the vector equation of a line passing through the point having the position vector 
and parallel to the line joining the points with position vectors 
and 
Also, find the Cartesian equivalents of this equation.
Given: line passes through the point with position vector 
and parallel to the line joining the points with position vectors 
and 
.
To find: equation of line in vector and Cartesian forms
Formula Used: Equation of a line is
Vector form: 
Cartesian form: 
where 
is a point on the line and 
with b1 : b2 : b3 being the direction ratios of the line.
Explanation:
Here, 
The direction ratios of the line are (1 - 2) : (-1 - 3) : (5 + 4)
⇒ -1 : -4 : 9
⇒ 1 : 4 : -9
So, 
Therefore,
Vector form:
Cartesian form:
1