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Definition and examples
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Vector Algebra
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Vector Operation
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Volume of pyramid determined by vectors calculator |
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- `(1,2,3), (3,0,6),(7,1,9)`
- `(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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Volume of pyramid 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 VolumePyramid(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 `=1/3|vec A * (vec B xx vec C)|`
1. Calculate scalar triple product
`A*(B xx C)`
`=|[A_1,A_2,A_3],[B_1,B_2,B_3],[C_1,C_2,C_3]|`
`=|[1,2,3],[3,0,6],[7,1,9]|`
`=1(0xx9-6xx1)-2(3xx9-6xx7)+3(3xx1-0xx7)`
`=1(0-6)-2(27-42)+3(3-0)`
`=1(-6)-2(-15)+3(3)`
`=-6+30+9`
`=33`
2. Calculate pyramid volume
Volume `=1/3 * 33=11`
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