Q. 185.0( 1 Vote )

Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.

and

Answer :

Given: Two lines are and



To find: Vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the given lines


The given lines are:




Formula used:


The vector equation of the line having normal and passing through point (the m, n, o) is given by,



The Cartesian equation of the line having normal and passing through point (the m, n, o) is given by,



Normal parallel to the line (1) is:



Normal parallel to the line (2) is:



The required line is perpendicular to the lines (1) and (2)


Hence, normal parallel to the required line is perpendicular to



Therefore,







Since required lines pass through the point (1, 2, -4)


Hence the vector equation of the required line is,




Put 12γ = k:



The Cartesian equation of the line is given by,



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