Example 14 - Find direction cosines of unit vector perpendicular - Examples

Example 14 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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Question 4 Find the direction cosines of the unit vector perpendicular to the plane .(6 3 2 ) + 1 = 0 passing through the origin. Vector equation of a plane at a distance d from the origin and unit vector to normal from origin is . = d Unit vector of = = 1 ( ) Given, equation of plane is .(6 3 2 ) + 1 = 0 .(6 3 2 ) = 1 Multiplying with 1 on both sides, .(6 3 2 ) = 1 1 . ( 6 + 3 + 2 ) = 1 So; = 6 + 3 + 2 Magnitude of = 6 2+32+22 = 36+9+4 = 49 = 7 Now, = 1 ( ) = 1 7 ( 6 + 3 + 2 ) = + + Direction cosines of unit vector perpendicular to the given plane i.e. in are , , .

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo