Find the equation of line in vector and in cartesian form that passes through the point with position vector and is in the direction
Step 1: Solve for the equation of the line in vector form
It is given that the line passes through the point with position vector and in the direction
Let is any line vector
Equation of a line through a point with position vector and parallel to is
where is an arbitrary constant
So the required equation of the line in vector form is
Equation of line in vector form is
Step 2: Solve for the equation of the line in cartesian form
General equation of line in cartesian form passing through point and having direction ratio is
Since the line passes through a point with position vector
Also line is in the direction of
Direction ratios are
Hence the equations of line in vector and cartesian form are and respectively.