GoldRush18
  • GoldRush18
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.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
To find the angle between vectors the dot product relation is used. \[\cos \theta=\frac{p*q}{\left| p \right|\left| q \right|}\]
anonymous
  • anonymous
So, this gives:\[\cos \theta=\frac{-3+48}{\sqrt{7}\sqrt{73}}\]\[\theta \approx75.15 \]degrees.
anonymous
  • anonymous
You should be able to get the area of the triangle POQ now

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anonymous
  • anonymous
|dw:1336587860891:dw|
anonymous
  • anonymous
let me know what you have so far
GoldRush18
  • GoldRush18
ok the page keeps refreshing thats why my replies are late
anonymous
  • anonymous
yeah sometimes this site chugs along bad
anonymous
  • anonymous
ah crap I made an error. the length of vector p should be sqrt(1+36)=sqrt(37)
GoldRush18
  • GoldRush18
ok im still working on the question
anonymous
  • anonymous
So the angle should be about 30 degrees
anonymous
  • anonymous
I got to get ready for work...good luck!
GoldRush18
  • GoldRush18
ok thanks so far bye

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