question_answer 1)

Find the vector and the Cartesian equations of the lines that passes through the origin and (5, –2, 3). 

Answer:

Let  be the position vectors of the points (0, 0, 0) and (5, ?2, 3)                         Let  be the position vector of any point on the line. Therefore, vector equation of line is                  i.e.       Putting             On equating, we get,             which is the required equation of line.