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

Solution:
Your problem `->` Volume of Parallelepiped (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 `=|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]|`

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

`=1(2xx(-4)-(-3)xx3)-3(1xx(-4)-(-3)xx(-2))+0(1xx3-2xx(-2))`

`=1(-8+9)-3(-4-6)+0(3+4)`

`=1(1)-3(-10)+0(7)`

`=1+30+0`

`=31`

2. Calculate parallelepiped volume
Volume `=31`






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