InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
दो सदिश ` vec a = 2hati + hatj + 3hatk " तथा" vec b = 3hati - 2hatj + hatk ` है | सिद्ध कीजिए की इनके बिच का कोण `60^(@)` है | |
|
Answer» ` vec a . vecb = (2hati + hatj + 3hatk). (3hati - 2hatj + hatk)` `= 6(hati.hati) -2 (hatj . hatj) +3(hatk . hatk )` ` = 6 - 2 + 3 = 7` `|veca| = |2hati + hatj + 3hatk = sqrt((2)^(2) + (1)^(2) + (3)^(2)] = sqrt(14)` तथा ` |vec b| = |3hati - 2 hatj + hatk | = sqrt([(3)^(2) +(-2 )^(2)(1)^(2)]) = sqrt(14)` अब , `cos theta = (veca.vecb)/(|veca|. |vecb|) = (7)/(sqrt(14) xx sqrt(14)) = (7)/(14) = (1)/(2)` ` rArr theta = cos^(-1) ((1)/(2)) rArr theta = 60^(2)` . |
|