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Definition and examples
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Vector Algebra
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Vector Operation
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Coplanar vectors calculator |
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- `(1,2,3), (4,5,6),(7,8,9)`
- `(1,2,3), (2,4,6),(3,4,5)`
- `(5,-1,1), (-2,3,4),(3,4,5)`
- `(5,6,1), (0,2,3),(3,4,5)`
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Solution
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Solution provided by AtoZmath.com
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Coplanar vectors calculator
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 1. `(1,2,3), (4,5,6),(7,8,9)`
2. `(1,2,3), (2,4,6),(3,4,5)`
3. `(5,-1,1), (-2,3,4),(3,4,5)`
4. `(5,6,1), (0,2,3),(3,4,5)`
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Example1. Find isCoplanar(A,B,C)
`A=(1,2,3)`,`B=(2,4,6)`,`C=(3,4,5)`
Solution:
Here `vec A=(1,2,3),vec B=(2,4,6),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]|`
`=|[1,2,3],[2,4,6],[3,4,5]|`
`=1(4xx5-6xx4)-2(2xx5-6xx3)+3(2xx4-4xx3)`
`=1(20-24)-2(10-18)+3(8-12)`
`=1(-4)-2(-8)+3(-4)`
`=-4+16-12`
`=0`
Here scalar triple product is zero, so vectors are coplanar
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