## GoldRush18 4 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.

1. anonymous

To find the angle between vectors the dot product relation is used. $\cos \theta=\frac{p*q}{\left| p \right|\left| q \right|}$

2. anonymous

So, this gives:$\cos \theta=\frac{-3+48}{\sqrt{7}\sqrt{73}}$$\theta \approx75.15$degrees.

3. anonymous

You should be able to get the area of the triangle POQ now

4. anonymous

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5. anonymous

let me know what you have so far

6. GoldRush18

ok the page keeps refreshing thats why my replies are late

7. anonymous

yeah sometimes this site chugs along bad

8. anonymous

ah crap I made an error. the length of vector p should be sqrt(1+36)=sqrt(37)

9. GoldRush18

ok im still working on the question

10. anonymous

So the angle should be about 30 degrees

11. anonymous

I got to get ready for work...good luck!

12. GoldRush18

ok thanks so far bye