Q. 74.5( 23 Votes )

The Cartesian equation of a line is . Write its vector form.

Answer :

We know that

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


Comparing this standard form with the given equation, we get


x1 = 5, y1 = -4, z1 = 6 and l = 3, m = 7, n = 2


The point through which the line passes has the position vector and the vector parallel to the line is given by .


Now, Vector equation of a line that passes through a given point whose position vector is and parallel to a given vector is .


The vector equation of the required line is:



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