माना `vec a =hati +hatj +hatk , vec a =4hati- 2hatj +3hatk `
और ` veca =hati -2hatj+ hatk ` तब ` 2veca -vecb +3vecc ` सदिश के समांतर एक ऐसा सदिश ज्ञात कीजिए जिसका परिमाण 6 इकाई है|

Explanation

दिया है ` : vec a = hati +hatj +hatk `
` " " vec b =4hat i-2hatj +3hatk `
और ` " " vec c =hati -2hatj +hatk`
` therefore" " 2veca -vecb +3vec c `
` =2 (hati +hatj +hatk ) -( 4hati -2hatj +3hatk )+ 3(hati -2hatj +hatk ) `
` =(2hat i + 2hatj +3hatk ) -( 4hati- 2hatj +3hatk )+ (3hati -6hatj + 3hatk ) `
` =2hati +2hatj +2hatk -4hati+2hatj -3hatk + 3hat i -6hat j + 3hat k = hati -2hat j +2hatk `
माना ` vec r =2vec a -vec b +3vecc =hati -2hatj +2hatk `
` therefore | vecr | =| hati -2j +3hatk |= sqrt(1^(2) +(-2) ^(2)+ 2^(2) ) =sqrt (9) =3`
अब सदिश ` vec r ` के अनुदिश मात्रक सदिश
` " "(vecr ) /(|vecr | ) =(hati-2hatj+ 2hatk )/( 3 ) = (1)/(3) hati -(2)/(3) hatj +(2)/(3) hatk `
` therefore ` अभीष्ट सदिश
` " " =6((1)/(3) hati -(2)/(3) hatj +(2)/(3) hatk ) `
` " " =2hati -4hatj+ 4hatk `