यदि `vec(a)=3hati-hatj+2hatk,vec(b)=2hati+hatj-hatk,vec(c)=hati-2hatj+2hatk, (vec(a)xx vec(b))xx vec(c)" तथा "vec(a)xx(vec(b)xx vec(c))` ज्ञात करें तथा उससे दिखाएँ कि `(vec(a)xxvec(b))xxc ne vec(a)xx(vec(b)xxvec( c ))`

Explanation

`vec(a)xxvec(b)=|{:(hati,,hatj,,hatk),(3,,-1,,2),(2,,1,,-1):}|=-hati+7hatj+5hatk`
`:.(vec(a)xxvec(b))xxvec(c)=(-hati+7hatj+5hatk)xx(hati-2hatj+2hatk)`
`=|{:(hati,,hatj,,hatk),(-1,,7,,5),(1,,-2,,2):}|=24hati+7hatj-5hatk" "...(1)`
पुन:, `vec(b)xxvec(c)=|{:(hati,,hatj,,hatk),(2,,1,,-1),(1,,-2,,2):}|`
`:. vec(a)xx(vec(b)xxvec(c))=(3hati-hatj+2hatk)xx(-5hatj-5hatk)`
`=|{:(hati,,hatj,,hatk),(3,,-1,,2),(0,,-5,,-5):}|=15(hati+hatj-hatk)" "...(2)`
(1) तथा (2) से स्पष्ट है कि,
`(vec(a)xxvec(b))xxvec(c)ne vec(a)xx(vec(b)xxvec(c))`