Question

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.

Answer 1

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

Answer 2

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

Answer 3

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