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Definition and examples
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Vector Algebra
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Vector Operation
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Area of triangle determined by two vectors calculator |
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- `(1,2,3), (4,5,6),(7,8,9)`
- `(5,-1,1), (-2,3,4),(3,4,5)`
- `(5,6,1), (0,2,3),(3,4,5)`
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Solution
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Solution provided by AtoZmath.com
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Area of triangle determined by two vectors calculator
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 1. `(1,2,3), (4,5,6),(7,8,9)`
2. `(5,-1,1), (-2,3,4),(3,4,5)`
3. `(5,6,1), (0,2,3),(3,4,5)`
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Example1. Find AreaTriangle(A,B)
`A=(1,2,3)`,`B=(4,5,6)`
Solution:
Here `vec A=(1,2,3),vec B=(4,5,6)`
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],[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)`
2. Calculate magnitude
`|vec vec A xx vec B|`
`=sqrt((-3)^2 + 6^2 + (-3)^2)`
`=sqrt(9 + 36 + 9)`
`=sqrt(54)`
`=7.3485`
3. Calculate triangle area
Area `=1/2 * 7.3485=3.6742`
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