Answer :

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:



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