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cory_ryan

  • 2 years ago

find the dot product v⋅w: for v=i-j, w=i+j

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  1. richyw
    • 2 years ago
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    \[\mathbf{v}\cdot\mathbf{w}=\langle 1,-1\rangle\cdot\langle 1,1\rangle\]\[=1(1)+-1(1)=0\]

  2. cory_ryan
    • 2 years ago
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    do you know how i would find the angle to that?

  3. richyw
    • 2 years ago
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    plot those two vectors onto a graph.

  4. cory_ryan
    • 2 years ago
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    ok and find the missing angle?

  5. richyw
    • 2 years ago
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    you can also use is the fact that for two vectors with magnitudes \(a\) and \(b\), with angle \(\theta\) between the two vectors, the dot product is\[\mathbf{a}\cdot\mathbf{b}=ab\cos{\theta}\]

  6. richyw
    • 2 years ago
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    so \(0=\cos{\theta}\)

  7. cory_ryan
    • 2 years ago
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    ok thats simple

  8. cory_ryan
    • 2 years ago
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    thanks bro

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