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GoldRush18

  • 3 years ago

The points P and Q have position vectors relative to the origin O given respectively by p=-i+6j and q=3i+8j. i. a) Calculate in degrees the size of the acute angle between p and q. b)hence, calculate the area of the triangle POQ ii Find in terms of i and j, the position vector of a) M, where M is the midpoint of PQ. b) R. where R is such that PQRO, labelled clockwise, forms a parallelogram.

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  1. eseidl
    • 3 years ago
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    To find the angle between vectors the dot product relation is used. \[\cos \theta=\frac{p*q}{\left| p \right|\left| q \right|}\]

  2. eseidl
    • 3 years ago
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    So, this gives:\[\cos \theta=\frac{-3+48}{\sqrt{7}\sqrt{73}}\]\[\theta \approx75.15 \]degrees.

  3. eseidl
    • 3 years ago
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    You should be able to get the area of the triangle POQ now

  4. eseidl
    • 3 years ago
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    |dw:1336587860891:dw|

  5. eseidl
    • 3 years ago
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    let me know what you have so far

  6. GoldRush18
    • 3 years ago
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    ok the page keeps refreshing thats why my replies are late

  7. eseidl
    • 3 years ago
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    yeah sometimes this site chugs along bad

  8. eseidl
    • 3 years ago
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    ah crap I made an error. the length of vector p should be sqrt(1+36)=sqrt(37)

  9. GoldRush18
    • 3 years ago
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    ok im still working on the question

  10. eseidl
    • 3 years ago
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    So the angle should be about 30 degrees

  11. eseidl
    • 3 years ago
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    I got to get ready for work...good luck!

  12. GoldRush18
    • 3 years ago
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    ok thanks so far bye

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