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anonymous

  • one year ago

Find a • b. a = 4i + 8j, b = -2i + 3j

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  1. welshfella
    • one year ago
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    this is the 'dot' product of 2 vectors a . b = 4i*-2i + 8j*3j

  2. welshfella
    • one year ago
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    its also called the Scalar product

  3. welshfella
    • one year ago
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    can you simplify this further?

  4. welshfella
    • one year ago
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    the square of the unit vectors i and j both = 1

  5. anonymous
    • one year ago
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    Okay. hmm

  6. anonymous
    • one year ago
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    -8,24

  7. anonymous
    • one year ago
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    @welshfella

  8. Empty
    • one year ago
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    @xamr Almost, but the dot product gives you a single value not a pair of values. So you need to ad those two numbers together. One application of the dot product is to calculate length which is the square root of the dot product, $$\text{length of vector a} = \sqrt{\vec a \cdot \vec a }$$

  9. anonymous
    • one year ago
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    So 16

  10. Empty
    • one year ago
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    Yep

  11. welshfella
    • one year ago
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    yes

  12. Jhannybean
    • one year ago
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    By thinking of i,j,k as components x,y,z we can rewrite vectors a and b. \[\vec a = \langle 4~,~8\rangle ~,~ \vec b = \langle -2~,~ 3\rangle\]

  13. anonymous
    • one year ago
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    Thank you all.

  14. welshfella
    • one year ago
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    yw

  15. Empty
    • one year ago
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    when you dot a vector with another vector, you get the amount of projection of one vector onto another. So if two vectors are at right angles to each other, then there's no projection at all, and the dot product is zero $$\vec a \cdot \vec b = 0 $$ means they're perpendicular to each other

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