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

Explanation

यहाँ, `vec(b)xxvec(c)=|{:(hati,,hatj,,hatk),(2,,-1,,1),(1,,1,,-2):}|=hati+5hatj+3hatk`
अब, `L.H.S.=vec(a)xx(vec(b)xxvec(c))=|{:(hati,,hatj,,hatk),(1,,2,,3),(1,,5,,3):}|.0`
`=-9hati+3hatk`
तथा `R.H.S.=(vec(a)cdot vec(c))vec(b)-(vec(a)cdot vec(b))vec(c)`
`=[1xx1+2xx(1)+3xx(-2)]vec(b)-[1xx2+2xx(-1)+3xx1]vec(c)`
`=-3(2hati-hatj+hatk)-3(hati+hatj-2hatk)`
`=-9hati+3hatk=L.H.S.`