Find the vector equation of a line passing through the point with position vector and parallel to the line joining the points with position vectors and Also, find the Cartesian equivalent of this equation.

direction ratios of the line joining the points with position vector and is ‹(1–1), (–1–1), (4–2)›

i. e. ‹0, –2, 2›

the vector equation of the line passing through the point with position vector and having direction ratio ‹0, –2, 2› is given as

Here x = 1, y = –2–2, z = –3 + 2

⇒

hence the cartesian equation of the line is