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# Find the equation of the line passing through the point and perpendicular to the lines and

Answer :

The vector equation of a line passing through a point with position vector and perpendicular to two lines with vector equations = + λ and = + λ, is given by = + λ() because as we know that vector product between two vectors will give you a vector whose direction is perpendicular to both the vectors, so the required equation is parallel to this vector and hence this is the equation.

Now we are given with,

= (+–3) and the lines perpendicular to required line are,

= +λ(2+–3) and = (2+)+μ(++)

= 2+–3 and = ++

Now,

=

=

=

Therefore, the required equation is,

= +–3 + ρ(4–5+)

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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