Last updated at May 29, 2018 by Teachoo

Transcript

Example 14 Find the direction cosines of the unit vector perpendicular to the plane šļ·Æ .(6 šļ·Æ ā 3 šļ·Æ ā 2 šļ·Æ) + 1 = 0 passing through the origin. Vector equation of a plane at a distance ādā from the origin and unit vector to normal from origin šļ·Æ is šļ·Æ . šļ·Æ = d Unit vector of šļ·Æ = šļ·Æ = 1ļ·® šļ·Æļ·Æļ·Æ( šļ·Æ) Given, equation of plane is šļ·Æ.(6 šļ·Æ ā 3 šļ·Æ ā 2 šļ·Æ) + 1 = 0 šļ·Æ.(6 šļ·Æ ā 3 šļ·Æ ā 2 šļ·Æ) = ā 1 Multiplying with ā1 on both sides, ā šļ·Æ.(6 šļ·Æ ā 3 šļ·Æ ā 2 šļ·Æ) = ā 1 Ć ā1 šļ·Æ. (ā6 šļ·Æ + 3 šļ·Æ + 2 šļ·Æ) = 1 So; šļ·Æ = ā 6 šļ·Æ + 3 šļ·Æ + 2 šļ·Æ Magnitude of šļ·Æ = ļ·® ā 6ļ·Æ2+32+22ļ·Æ šļ·Æļ·Æ = ļ·®36+9+4ļ·Æ = ļ·®49ļ·Æ = 7 Now, šļ·Æ = 1ļ·® šļ·Æļ·Æļ·Æ ( šļ·Æ) = 1ļ·®7ļ·Æ (ā 6 šļ·Æ + 3 šļ·Æ + 2 šļ·Æ) = āšļ·®šļ·Æ šļ·Æ + šļ·®šļ·Æ šļ·Æ + šļ·®šļ·Æ šļ·Æ ā“ Direction cosines of unit vector perpendicular to the given plane i.e. in are ā šļ·®šļ·Æ, šļ·®šļ·Æ , šļ·®šļ·Æ .

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Example 14 You are here

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Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.