यदि `vec(a)=hati-hatj-3hatk,vec(b)=4hati-3hatj+hatk" तथा "vec(c)=2hati-hatj+2hatk`, सत्यापित करें कि `vec(a)xx(vec(b)+vec(c))=vec(a)xx vec(b)+vec(a)xx vec(c)`

Explanation

दिया है, `vec(a)=hati-hatj-3hatk,vec(b)=4hati-3hatj+hatk" तथा "vec(c)=2hati-hatj+2hatk`.
अब, `vec(b)+vec(c)=(4hati-3hatj+hatk)+(2hati-hatj+2hatk)`
`=6hati-4hatj+3hatk`
`:.vec(a)xx(vec(b)+vec(c))=|{:(hati,,hatj,,hatk),(1,,-1,,-3),(6,,-4,,3):}|`
`=(-3-12)hati-(3+18)hatj+(-4+6)hatk`
`=-15hati-21hatj+2hatk" "...(1)`
पुन:, `vec(a)xx vec(b)=|{:(hati,,hatj,,hatk),(1,,-1,,-3),(4,,-3,,1):}|=(-1-9)hati-(1+12)hatj+(-3+4)hatk`
`=-10hati-13hatj+hatk`
तथा `vec(a)xx vec(c)=|{:(hati,,hatj,,hatk),(1,,-1,,-3),(2,,-1,,2):}|=(-2-3)hati-(2+6)hatj+(-1+2)hatk`
`=-5hati-8hatj+hatk`
`:. vec(a)xx vec(b)+vec(a)xx vec(c)=(-10hati-13hatj+hatk)+(-5hati-8hatj+hatk)`
`=-15hati-21hatj+2hatk" "...(2)`
(1) तथा (2) से, हमें मिलता है
`vec(a)xx(vec(b)+vec(c))=vec(a)xx vec(b)+vec(a)xx vec(c)`