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

We know that

Vector equation of a line that passes through a given point whose position vector is and parallel to a given vector is .

So, here the position vector of the point (1, 2, 3) is given by and the parallel vector is .

∴ The vector equation of the required line is:

, where is a real number.

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