Q. 204.0( 21 Votes )

Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines:

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, -4)


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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