Find the Cartesian and vector equations of a line which passes through the point (1, 2, 3) and is parallel to the line

Given: line passes through (1, 2, 3) and is parallel to the line



To find: equation of line in Vector and Cartesian form


Formula Used: Equation of a line is


Vector form:


Cartesian form:


where is a point on the line and is a vector parallel to the line.


Explanation:


Since the line (say L1) is parallel to another line (say L2), L1 has the same direction ratios as that of L2


Here,


Equation of L2 can be rewritten as:





Therefore,


Vector form of the line is:



Cartesian form of the line is:



1