Q. 194.1( 35 Votes )

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes s and .

Answer :

The vector equation of a line passing through a point with position vector and parallel to a vector is


Given, the line passes through (1,2,3)


So,


Given, line is parallel to both planes


Line is perpendicular to normal of both planes.


i.e is perpendicular to normal of both planes.


we know that -


is perpendicular to both &


So, is cross product of normals of planes


and


Required Normal





Thus,


Now, putting the value of & in formula




Therefore, the equation of the line is



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