2. Example-2
1. Find isCoplanar(A,B,C)
`A=(1,2,3)`,`B=(4,5,6)`,`C=(7,8,9)`
Solution:
Here `vec A=(1,2,3),vec B=(4,5,6),vec C=(7,8,9)`
The 3 vectors are coplanar, if their scalar triple product is zero
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],[4,5,6],[7,8,9]|`
`=1(5xx9-6xx8)-2(4xx9-6xx7)+3(4xx8-5xx7)`
`=1(45-48)-2(36-42)+3(32-35)`
`=1(-3)-2(-6)+3(-3)`
`=-3+12-9`
`=0`
Here scalar triple product is zero, so vectors are coplanar
2. Find ISCOPLANAR(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)`
The 3 vectors are coplanar, if their scalar triple product is zero
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``!=0`
Here scalar triple product is not zero, so vectors are not coplanar
This material is intended as a summary. Use your textbook for detail explanation.
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