Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line 
Also, find the distance between these lines.
HINT: The given line is
The required line is
Now, find the distance between the parallel lines L1 and L2.
Given : point A ≡ (2, 3, 2)
Equation of line : 
To Find : i) equation of line
ii) distance d
Formulae :
1. Equation of line :
Equation of line passing through point A (a1, a2, a3) and parallel to vector 
is given by
Where, 
2. Cross Product :
If 
are two vectors
then,
3. Dot Product :
If 
are two vectors
then,
4. Shortest distance between two parallel lines :
The shortest distance between the parallel lines 
and
is given by,
Answer :
As the required line is parallel to the line
Therefore, the vector parallel to the required line is
Given point A ≡ (2, 3, 2)
Therefore, equation of line passing through A and parallel to 
is
Now, to calculate distance between above line and given line,
Here,
= 7
Therefore, the shortest distance between the given lines is
