If ` vec a=2 hat i+5 hat j=7 hat k , vec b=-3 hat j+ hat k"and" vecc= hat i-2 hat j-3 hat k ,` compute `( veca xx vecb) xx vecc` and ` veca xx ( vecb xx vecc)` and verify that these are not equal.

Explanation

`veca xx vecb = |[hati,hatj,hatk],[2,5,-7],[-3,4,1]|`

`veca xx vecb = 33hati+19hatj+23hatk`

Now, `(veca xx vecb) xx vecc =|[hati,hatj,hatk],[33,19,23],[1,-2,-3]| = -11hati+122hatj-85hatk`



Now, `vecb xx vecc = |[hati,hatj,hatk],[-3,4,1],[1,-2,-3]| = -10hati-8hatj+2hatk`

Now, `veca xx (vecb xx vecc) = |[hati,hatj,hatk],[2,5,-7],[-10,-8,2]| = -46hati+66hatj+34hatk`

Thus, `(veca xx vecb) xx vecc != veca xx (vecb xx vecc).`