1. Example-1
1. 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`
2. Find VolumeParallelepiped(A,B,C)
`A=(5,-1,1)`,`B=(-2,3,4)`,`C=(3,4,5)`
Solution:
Here `vec A=(5,-1,1),vec B=(-2,3,4),vec C=(3,4,5)`
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]|`
`=|[3,4,5],[5,-1,1],[-2,3,4]|`
`=3((-1)xx4-1xx3)-4(5xx4-1xx(-2))+5(5xx3-(-1)xx(-2))`
`=3(-4-3)-4(20+2)+5(15-2)`
`=3(-7)-4(22)+5(13)`
`=-21-88+65`
`=-44`
2. Calculate parallelepiped volume
Volume `=44`
This material is intended as a summary. Use your textbook for detail explanation.
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