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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)`
4. `(0,2,3),(5,6,1),(1,5,6)`
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Example (with steps)1. Find Volume of Parallelepiped determined by vectors `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 A * (vec B xx vec C)|` 1. Calculate scalar triple product `vec A * (vec B xx vec C)` | = | | `1` | `2` | `3` | | | `3` | `0` | `6` | | | `7` | `1` | `9` | |
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`=1 xx (0 xx 9 - 6 xx 1) -2 xx (3 xx 9 - 6 xx 7) +3 xx (3 xx 1 - 0 xx 7)` `=1 xx (0 -6) -2 xx (27 -42) +3 xx (3 +0)` `=1 xx (-6) -2 xx (-15) +3 xx (3)` `= -6 +30 +9` `=33` 2. Calculate parallelepiped volume Volume `=33`
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