Find the vector equation of a line passing through the point A(3, -2, 1) and parallel to the line joining the points B(-2, 4, 2) and C(2, 3, 3). Also, find the Cartesian equations of the line.
Given: line passes through the point (3, -2, 1) and is parallel to the line joining points B(-2, 4, 2) and C(2, 3, 3).
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 (-2 - 2) : (4 - 3) : (2 - 3)
⇒ -4 : 1 : -1
⇒ 4 : -1 : 1
So, 
Therefore,
Vector form:
Cartesian form:
1