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 (x_{1}, y_{1}, z_{1}) and having direction cosines l, m, n is .

Comparing this standard form with the given equation, we get

x_{1} = 5, y_{1} = -4, z_{1} = 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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Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.

and

Mathematics - Board PapersWrite the vector equations of the following lines and hence determine the distance between them:

Mathematics - Board Papers