InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
5 इकाई मापांक वाला वह सदिश ज्ञात कीजिए जो प्रत्येक ` (veca + vecb ) " तथा" (veca - vecb) ` से लम्बवत हो , जहाँ ` veca = (hati + hatj + hatk) " तथा" vecb = (hati + 2hatj + 3hatk) ` है | |
|
Answer» यहां दिया है `veca = (hati + hatj + hatk ) " तथा " vecb = (hati + 2hatj + 3hatk) ` , तब `(veca + vecb )= (hati + hatj + hatk ) + (hati + 2hatj + 3hatk ) = (2hati + 3hatj + 4hatk)` तथा `(veca - vecb )= (hati + hatj + hatk ) - (hati + 2hatj + 3hatk ) = ( -hatj + 2hatk)` ` therefore (veca + vecb )xx (veca - vecb )= |{:(hati , hatj , hatk),(2,3,4),(0, -1, -2):}|` `= (-6 + 4)hati - (-4-0)hatj + (-2 -0)hatk` ` = (- 2hati + 4hatj - 2hatk)` अब ` therefore (veca + vecb )xx (veca - vecb )| = sqrt((-2)^(2) + 4^(2) + (-2)^(2))` ` = sqrt(24) = 2sqrt(6)` अतः अभीष्ट सदिश `=pm (5{(veca + vecb)xx(veca - vecb)})/(|(veca + vecb)xx(veca - vecb)|)` `= pm (5 (-2hati + 4hatj - 2hatk))/(2sqrt(6))` ` = pm (5(-hati + 2hatj - hatk))/(sqrt(6))` . |
|