Answer :

__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 L_{1}) is parallel to another line (say L_{2}), L_{1} has the same direction ratios as that of L_{2}

Here,

Since the equation of L_{2} is

Therefore,

Vector form of the line is:

Cartesian form of the line is:

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