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GoldRush18
 2 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.
GoldRush18
 2 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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eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0To find the angle between vectors the dot product relation is used. \[\cos \theta=\frac{p*q}{\left p \right\left q \right}\]

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0So, this gives:\[\cos \theta=\frac{3+48}{\sqrt{7}\sqrt{73}}\]\[\theta \approx75.15 \]degrees.

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0You should be able to get the area of the triangle POQ now

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0let me know what you have so far

GoldRush18
 2 years ago
Best ResponseYou've already chosen the best response.0ok the page keeps refreshing thats why my replies are late

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0yeah sometimes this site chugs along bad

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0ah crap I made an error. the length of vector p should be sqrt(1+36)=sqrt(37)

GoldRush18
 2 years ago
Best ResponseYou've already chosen the best response.0ok im still working on the question

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0So the angle should be about 30 degrees

eseidl
 2 years ago
Best ResponseYou've already chosen the best response.0I got to get ready for work...good luck!

GoldRush18
 2 years ago
Best ResponseYou've already chosen the best response.0ok thanks so far bye
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