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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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