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Volume of Parallelepiped determined by vectors calculator
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1. `(1,2,3), (3,0,6),(7,1,9)`
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 VolumeParallelepiped(A,B,C) `A=(1,2,3)`,`B=(3,0,6)`,`C=(7,1,9)`
Solution: Here `vec A=(1,2,3),vec B=(3,0,6),vec C=(7,1,9)`
Volume `=|vec C * (vec A xx vec B)|`
1. Calculate scalar triple product `C*(A xx B)`
`=|[C_1,C_2,C_3],[A_1,A_2,A_3],[B_1,B_2,B_3]|`
`=|[7,1,9],[1,2,3],[3,0,6]|`
`=7(2xx6-3xx0)-1(1xx6-3xx3)+9(1xx0-2xx3)`
`=7(12-0)-1(6-9)+9(0-6)`
`=7(12)-1(-3)+9(-6)`
`=84+3-54`
`=33`
2. Calculate parallelepiped volume Volume `=33`
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