## GoldRush18 Group Title 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. 2 years ago 2 years ago

1. eseidl Group Title

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 Group Title

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

3. eseidl Group Title

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

4. eseidl Group Title

|dw:1336587860891:dw|

5. eseidl Group Title

let me know what you have so far

6. GoldRush18 Group Title

ok the page keeps refreshing thats why my replies are late

7. eseidl Group Title

yeah sometimes this site chugs along bad

8. eseidl Group Title

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

9. GoldRush18 Group Title

ok im still working on the question

10. eseidl Group Title

So the angle should be about 30 degrees

11. eseidl Group Title

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

12. GoldRush18 Group Title

ok thanks so far bye