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Problem: Area of parallelogram (1,2,-3),(-2,3,-4) [ Calculator, Method and examples ]

Solution:
Your problem `->` Area of parallelogram (1,2,-3),(-2,3,-4)


Here `vec A=(1,2,-3),vec B=(-2,3,-4)`

Area `=|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],[1,2,-3],[-2,3,-4]|`

`=i(2xx(-4)-(-3)xx3)-j(1xx(-4)-(-3)xx(-2))+k(1xx3-2xx(-2))`

`=i(-8+9)-j(-4-6)+k(3+4)`

`=i+10j+7k`

`=(1,10,7)`

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

`=sqrt(1^2 + 10^2 + 7^2)`

`=sqrt(1 + 100 + 49)`

`=sqrt(150)`

`=12.2474`


3. Calculate triangle area
Area `= 12.2474`






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