The Cartesian equations of a line are 
Find its vector equation.
Given : A line 
To find : vector equation of a line 
Formula used : If a line is given by 
= 
= 
= λ then vector equation of the line is given by 
= a
+ b
+ c
+ λ (l
+ m
+ n
)
The given line is 
= 
= 
Here a = 1 , b = -2 , c = 5 and l = 2 , m = 3 , n = -1
Substituting the above values,we get
= 1
- 2
+ 5
+ λ (2
+ 3
- 1
)
The vector equation of a line 
is given by
= 1
- 2
+ 5
+ λ (2
+ 3
- 1
)
1