Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12th

Q. No. 20 of Miscellaneous Exercise

Listen NCERT Audio Books - Kitabein Ab Bolengi

20

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

and .

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



20

Chapter Exercises

More Exercise Questions

6

If the lines and are perpendicular, find the value of k.