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 .

Here, and

⇒ The vector equation of the required line is:

⇒

Also, we know that

The Cartesian equation of a line through a point (x₁, y₁, z₁) and having direction cosines l, m, n is .

Also, we know that if the direction ratios of the line are a, b, c, then

⇒

⇒ The Cartesian equation of a line through a point (x₁, y₁, z₁) and having direction ratios a, b, c is .

Here, x₁ = 2, y₁ = -1, z₁ = 4 and a = 1, b = 2, c = -1

⇒ The Cartesian equation of the required line is:

⇒