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Definition and examples
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Vector Algebra
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Vector Operation
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Vector projections of B onto A calculator |
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- `(3,4), (4,3)`
- `(1,2), (3,4)`
- `(3,4,0), (2,2,1)`
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Solution
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Solution provided by AtoZmath.com
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Vector projections of B onto A calculator
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 1. `(3,4), (4,3)`
2. `(1,2), (3,4)`
3. `(3,4,0), (2,2,1)`
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Example1. Find projection(A,B)
`A=(3,4,0)`,`B=(2,2,1)`
Solution:
Here `vec A=(3,4,0),vec B=(2,2,1)`
`proj_(vec B)vec A=(vec A * vec B)/|vec B|^2 * vec B`
1. Calculate dot product
`vec A * vec B`
`=A_1*B_1 + A_2*B_2 + A_3*B_3`
`=3*2 + 4*2 + 0*1`
`=6 + 8 + 0`
`=14`
2. Calculate magnitude
`|vec B|`
`=sqrt(B_1^2 + B_2^2 + B_3^2)`
`=sqrt(2^2 + 2^2 + 1^2)`
`=sqrt(4 + 4 + 1)`
`=sqrt(9)`
`=3`
`:.|vec B|^2=9`
The Vector projection is given by
`proj_(vec B)vec A=(vec A * vec B)/|vec B|^2 * vec B`
`=(14)/(9) * vec B`
`=(14)/(9) * (2,2,1)`
`=(28/9,28/9,14/9)`
The scalar projection is given by
`proj_(vec B)vec A=(vec A * vec B)/|vec B|`
Now, `(vec A * vec B)/(|vec B|)`
`=14/3`
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