मान लीजिए सदिश ` veca , vecb , vecc` क्रमश : ` a_(1) hati + a_(2) hatj + a _(3) hatk , b_(2) hatj + b_(3) hatk , c _(1) hati + c_(2) hatj + c_(3) hatk

दिया है , ` veca = a_(1) hati + a_(2) hatj + a_(3) hatk` ,
` vecb = b _(1) hati + b_(2) hatj b_(3) hatk`
तथा ` vecc = c_(1) hati + c_(2) hatj C_(3) hatk `
अब ` vecb + vecc = ( b_(1) + c_(1) ) hati +( b_(2) + c_(2) ) hatj +( b_(3) + c_(3)) hatk`
` therefore veca xx ( vecb + vecc)=|{:( hati , hatj , hatk ) ,( a_(1) ,a_(2) , a_(3) ),( b_(1) + c_(1) ,b_(2) + c_(2) , b_(3) + c_(3)):}|`
` = |{:( hati , hatj , hatk) ,( a_(1) , a_(2) , a_(3)),( b_(1) , b_(2) b_(3)):}|+|{: ( hati , hatj , hatk ) ,( a_(1), a_(2) ,a_(3)),( c_(1),c_(2) , c_(3)):}|...(1)`
( सारणिक के गुणधर्म द्वारा )
` = veca xx vecb + veca xx vecc`