Find the equation of the line passing through the point (2, –1, 3) and parallel to the line
Vector equation of a line is 
where 
is the position vector of the point a through which our line passes through and 
is the vector parallel to our line and 
is the general vector of a line satisfying these conditions and 
is a constant.
Now the point vector through which the line passes is 
= 2
+3
and the required line is parallel to a line having vector equation,
= (
–2
+
) + λ(2
+3
–5
)
The parallel vector is,
= (2
+3
–5
)
So the vector equation of the required line is,
= (2
+3
) + μ(2
+3
–5
)
Where μ is a constant or a scalar.
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