2. Example-2
1. Find VolumePyramid(A,B,C)
`A=(5,6,1)`,`B=(0,2,3)`,`C=(3,4,5)`
Solution:
Here `vec A=(5,6,1),vec B=(0,2,3),vec C=(3,4,5)`
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]|`
`=|[5,6,1],[0,2,3],[3,4,5]|`
`=5(2xx5-3xx4)-6(0xx5-3xx3)+1(0xx4-2xx3)`
`=5(10-12)-6(0-9)+1(0-6)`
`=5(-2)-6(-9)+1(-6)`
`=-10+54-6`
`=38`
2. Calculate pyramid volume
Volume `=1/3 * 38=12.6667`
2. Find VOLUMEPYRAMID(A,B,C)
`A=(0,2,3)`,`B=(5,6,1)`,`C=(1,5,6)`
Solution:
Here `vec A=(0,2,3),vec B=(5,6,1),vec C=(1,5,6)`
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]|`
`=|[0,2,3],[5,6,1],[1,5,6]|`
`=0(6xx6-1xx5)-2(5xx6-1xx1)+3(5xx5-6xx1)`
`=0(36-5)-2(30-1)+3(25-6)`
`=0(31)-2(29)+3(19)`
`=0-58+57`
`=-1`
2. Calculate pyramid volume
Volume `=1/3 * 1=1/3`
This material is intended as a summary. Use your textbook for detail explanation.
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