Slide25.JPG

Slide26.JPG
Slide27.JPG

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
Ask Download

Transcript

Ex 10.5 , 7 (Supplementary NCERT) Show that vectors ๐‘Žย โƒ—, ๐‘ย โƒ— and ๐‘ย โƒ— are coplanar if ๐‘Žย โƒ— + ๐‘ย โƒ—, ๐‘ย โƒ— + ๐‘ and ๐‘ย โƒ— + ๐‘Žย โƒ— are coplanarEx 10.5 , 7 (Supplementary NCERT) Show that vectors ๐‘Žย โƒ—, ๐‘ย โƒ— and ๐‘ย โƒ— are coplanar if ๐‘Žย โƒ— + ๐‘ย โƒ—, ๐‘ย โƒ— + ๐‘ and ๐‘ย โƒ— + ๐‘Žย โƒ— are coplanarGiven ๐‘Žย โƒ— + ๐‘ย โƒ—, ๐‘ย โƒ— + ๐‘ and ๐‘ย โƒ— + ๐‘Žย โƒ— are coplanar [โ– 8(๐‘Žย โƒ—" + " ๐‘ย โƒ—&๐‘ย โƒ—+๐‘ย โƒ—&๐‘ย โƒ—+๐‘Žย โƒ— )] = 0 We need to prove ๐‘Žย โƒ—, ๐‘ย โƒ— and ๐‘ย โƒ— are coplanar i.e. [โ– 8(๐‘Žย โƒ—&๐‘ย โƒ—&๐‘ย โƒ— )] = 0 Now, [โ– 8(๐‘Žย โƒ—" + " ๐‘ย โƒ—&๐‘ย โƒ—+๐‘ย โƒ—&๐‘ย โƒ—+๐‘Žย โƒ— )] = 0 (๐‘Žย โƒ—" + " ๐‘ย โƒ—). ["(" ๐‘ย โƒ—+๐‘ย โƒ—") " ร— " (" ๐‘ย โƒ—+๐‘Žย โƒ—)] = 0 (๐‘Žย โƒ—" + " ๐‘ย โƒ—). ["(" ๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘Žย โƒ—)+"(" ๐’„ย โƒ—ร—๐’„ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘Žย โƒ—)] = 0 ๐‘ย โƒ— ร— ๐‘ย โƒ— = |๐‘ย โƒ— ||๐‘ย โƒ— | sin 0 ๐‘›ย ฬ‚ = 0 "(" ๐‘Žย โƒ—+๐‘ย โƒ—")." [(๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘Žย โƒ— ) "+ 0 + (" ๐‘ย โƒ—" ร— " ๐‘Žย โƒ—") " ] = 0 "(" ๐‘Žย โƒ—+๐‘ย โƒ—")." [(๐‘ย โƒ—ร—๐‘ย โƒ—") + (" ๐‘ย โƒ—ร—๐‘Žย โƒ— ) "+ (" ๐‘ย โƒ—" ร— " ๐‘Žย โƒ—") " ] = 0 ๐‘Žย โƒ—. (๐‘ย โƒ— ร— ๐‘ย โƒ—) + ๐‘ย โƒ—.(๐‘ย โƒ— ร— ๐‘ย โƒ—) + ๐‘Žย โƒ—. (๐‘ย โƒ— ร— ๐‘Žย โƒ—) + ๐‘ย โƒ—.(๐‘ย โƒ— ร— ๐‘Žย โƒ—) + ๐‘Žย โƒ—.(๐‘ย โƒ— ร— ๐‘Žย โƒ—) + ๐‘ย โƒ—.(๐‘ย โƒ— ร— ๐‘Žย โƒ—) = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’ƒย โƒ—", " ๐’ƒย โƒ—", " ๐’„ย โƒ— ] + [๐’‚ย โƒ—", " ๐’ƒย โƒ—", " ๐’‚ย โƒ— ] + [๐’ƒย โƒ—", " ๐’ƒย โƒ—", " ๐’‚ย โƒ— ] + [๐’‚ย โƒ—", " ๐’„ย โƒ—", " ๐’‚ย โƒ— ] + [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘Žย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + 0 + 0 + 0 + 0 + [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘Žย โƒ— ] = 0 [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = ๐‘ย โƒ—. (๐‘ย โƒ— ร— ๐‘ย โƒ—) As (๐‘ย โƒ— ร— ๐‘ย โƒ—) = 0ย โƒ— = ๐‘ย โƒ— . 0ย โƒ— = 0ย โƒ— Using Prop: [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘Žย โƒ— ] = 0 [๐‘ย โƒ—", " ๐‘ย โƒ—", " ๐‘Žย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘Žย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’ƒย โƒ—", " ๐’„ย โƒ—", " ๐’‚ย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] + [๐’‚ย โƒ—", " ๐’ƒย โƒ—", " ๐’„ย โƒ— ] = 0 2[๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = 0 [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = 0 Since [๐‘Žย โƒ—", " ๐‘ย โƒ—", " ๐‘ย โƒ— ] = 0, ๐’‚ย โƒ—, ๐’ƒย โƒ— and ๐’„ย โƒ— are coplanar

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.