1. Find VECTORTRIPLEPRODUCT(A,B,C)
`A=(1,2,3)`,`B=(4,5,6)`,`C=(2,6,5)`

Solution:
Here `vec A=(1,2,3),vec B=(4,5,6),vec C=(2,6,5)`


1. Calculate `Axx(BxxC)`

`vec B xx vec C`

`=|[i,j,k],[B_1,B_2,B_3],[C_1,C_2,C_3]|`

`=|[i,j,k],[4,5,6],[2,6,5]|`

`=i(5xx5-6xx6)-j(4xx5-6xx2)+k(4xx6-5xx2)`

`=i(25-36)-j(20-12)+k(24-10)`

`=-11i-8j+14k`

`=(-11,-8,14)`

`vec A xx vec (B xx C)`

`=|[i,j,k],[A_1,A_2,A_3],[(B xx C)_1,(B xx C)_2,(B xx C)_3]|`

`=|[i,j,k],[1,2,3],[-11,-8,14]|`

`=i(2xx14-3xx(-8))-j(1xx14-3xx(-11))+k(1xx(-8)-2xx(-11))`

`=i(28+24)-j(14+33)+k(-8+22)`

`=52i-47j+14k`

`=(52,-47,14)`

---

2. Calculate `(AxxB)xxC)`

`vec A xx vec B`

`=|[i,j,k],[A_1,A_2,A_3],[B_1,B_2,B_3]|`

`=|[i,j,k],[1,2,3],[4,5,6]|`

`=i(2xx6-3xx5)-j(1xx6-3xx4)+k(1xx5-2xx4)`

`=i(12-15)-j(6-12)+k(5-8)`

`=-3i+6j-3k`

`=(-3,6,-3)`

`vec (A xx B) xx vec C`

`=|[i,j,k],[(A xx B)_1,(A xx B)_2,(A xx B)_3],[C_1,C_2,C_3]|`

`=|[i,j,k],[-3,6,-3],[2,6,5]|`

`=i(6xx5-(-3)xx6)-j((-3)xx5-(-3)xx2)+k((-3)xx6-6xx2)`

`=i(30+18)-j(-15+6)+k(-18-12)`

`=48i+9j-30k`

`=(48,9,-30)`