Slide16.JPG

Slide17.JPG

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

Transcript

Ex 10.5, 4 (Supplementary NCERT) Let ๐‘Žย โƒ— = ๐‘–ย ฬ‚ + ๐‘—ย ฬ‚ + ๐‘˜ย ฬ‚, ๐‘ย โƒ— = ๐‘–ย ฬ‚ and ๐‘ย โƒ— = c1๐‘–ย ฬ‚ + c2๐‘—ย ฬ‚ + c3๐‘˜ย ฬ‚ are coplanar (a) If c1 = 1 and c2 = 2, find c3 which makes ๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— coplanar Given c1 = 1 and c2 = 2 So, ๐‘Žย โƒ— = ๐‘–ย ฬ‚ + ๐‘—ย ฬ‚ + ๐‘˜ย ฬ‚ ๐‘ย โƒ— = ๐‘–ย ฬ‚ = ๐‘–ย ฬ‚ + 0๐‘—ย ฬ‚ + 0๐‘˜ย ฬ‚ ๐‘ย โƒ— = c1๐‘–ย ฬ‚ + c2๐‘—ย ฬ‚ + c3๐‘˜ย ฬ‚ = 1๐‘–ย ฬ‚ + 2๐‘—ย ฬ‚ + c3๐‘˜ย ฬ‚ Three vectors ๐‘Žย โƒ—, ๐‘ย โƒ—, ๐‘ย โƒ— are coplanar if [๐’‚ย โƒ—" " ๐’ƒย โƒ—" " ๐’„ย โƒ— ] = 0 Finding [๐’‚ย โƒ—" " ๐’ƒย โƒ—" " ๐’„ย โƒ— ] [๐‘Žย โƒ—" " ๐‘ย โƒ—" " ๐‘ย โƒ— ] = |โ– 8(1&1&1@1&0&0@1&2&๐‘_3 )| 0 = 1[(0ร—๐‘_3 )โˆ’(0ร—2) ] โˆ’ 1[(1ร—๐‘_3 )โˆ’(1ร—0) ] + 1[(1ร—2)โˆ’(1ร—0) ] 0 = 1 [0โˆ’0]โˆ’1[๐‘_3โˆ’0]+1[2โˆ’0] 0 = 0 โ€“ ๐‘_3 + 2 0 = โ€“ ๐‘_3 + 2 ๐’„_๐Ÿ‘ = 2 Therefore, ๐‘Žย โƒ—,๐‘,๐‘ย โƒ— are coplanar if ๐‘_3 = 2

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.