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.