Q. 165.0( 1 Vote )

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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