1. Find Area of triangle determined by two vectors
`A=(5,6,1)`, `B=(0,2,3)`

Solution:
Here `vec A=(5,6,1),vec B=(0,2,3)`

Area `=1/2|vec A xx vec B|`

1. Calculate cross product
`vec A xx vec B`

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

`=|[i,j,k],[5,6,1],[0,2,3]|`

`=i(6xx3-1xx2)-j(5xx3-1xx0)+k(5xx2-6xx0)`

`=i(18-2)-j(15-0)+k(10-0)`

`=16i-15j+10k`

`=(16,-15,10)`

2. Calculate magnitude
`|vec vec A xx vec B|`

`=sqrt(16^2 + (-15)^2 + 10^2)`

`=sqrt(256 + 225 + 100)`

`=sqrt(581)`


3. Calculate triangle area
Area `=1/2 * sqrt(581)=(sqrt(581))/2`

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2. Find Area of triangle determined by two vectors
`A=(0,2,3)`, `B=(3,4,5)`

Solution:
Here `vec A=(0,2,3),vec B=(3,4,5)`

Area `=1/2|vec A xx vec B|`

1. Calculate cross product
`vec A xx vec B`

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

`=|[i,j,k],[0,2,3],[3,4,5]|`

`=i(2xx5-3xx4)-j(0xx5-3xx3)+k(0xx4-2xx3)`

`=i(10-12)-j(0-9)+k(0-6)`

`=-2i+9j-6k`

`=(-2,9,-6)`

2. Calculate magnitude
`|vec vec A xx vec B|`

`=sqrt((-2)^2 + 9^2 + (-6)^2)`

`=sqrt(4 + 81 + 36)`

`=sqrt(121)`

`=11`


3. Calculate triangle area
Area `=1/2 * 11=11/2`

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