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katherinekc

  • 3 years ago

Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 7>, v = <9, 7>

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  1. ZeHanz
    • 3 years ago
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    You could use the formula:\[\cos \theta=\frac{ \vec u \cdot \vec v}{ |\vec u||\vec v| }\]assuming you are familiar with the dot product of vectors.

  2. Sshmoo
    • 3 years ago
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    here it is on mathematica.

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  3. katherinekc
    • 3 years ago
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    that wouldnt let me open it @Sshmoo

  4. katherinekc
    • 3 years ago
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    im just learning it so im still so comfused

  5. Sshmoo
    • 3 years ago
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    i'll try converting it to a different file, all it is is a graph of the vectors and a dot product. It just looks shinier.

  6. katherinekc
    • 3 years ago
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    ohok

  7. Sshmoo
    • 3 years ago
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    here it is in PDF

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  8. katherinekc
    • 3 years ago
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    okk hm so

  9. katherinekc
    • 3 years ago
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    so which of these would the answer be ? -8.3° 1.7° 3.3° 13.3°

  10. ZeHanz
    • 3 years ago
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    If you calculate cos theta, you get: \[\cos \theta=\frac{ 8 \cdot 9 + 7 \cdot 7 }{ \sqrt{8^2+7^2}\sqrt{9^2+7^2} }=\frac{ 72+49 }{\sqrt{113}\sqrt{130} }=\frac{ 121 }{ \sqrt{113} \sqrt{130}}\approx 0.99833\]Now take the inverse cosine (cos^-1 on your calculator) to see the answer.

  11. katherinekc
    • 3 years ago
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    THANK YOU!

  12. ZeHanz
    • 3 years ago
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    yw!

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