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Problem: Volume of pyramid (1,2,-3),(-2,3,-4),(1,3,0) [ Calculator, Method and examples ]

Solution:
Your problem `->` Volume of pyramid (1,2,-3),(-2,3,-4),(1,3,0)


Here `vec A=(1,2,-3),vec B=(-2,3,-4),vec C=(1,3,0)`

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],[-2,3,-4],[1,3,0]|`

`=1(3xx0-(-4)xx3)-2((-2)xx0-(-4)xx1)+-3((-2)xx3-3xx1)`

`=1(0+12)-2(0+4)+-3(-6-3)`

`=1(12)-2(4)+-3(-9)`

`=12-8+27`

`=31`

2. Calculate pyramid volume
Volume `=1/3 * 31=31/3`






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