Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and . is in the direction

Solution:

Given:
Vector equation of a line that passes through a given point whose position vector is and parallel to a given vector is
Let, and
Therefore, the vector equation of the required line is:

The Cartesian eq. of a line through a point and having direction cosines is given by

Here, and
The Cartesian equation of the required line is: