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 |

Explanation

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))` .