This is a fairly simple thing to do, but what would be the optimal approach to solve part (c) (parts (a) and (b) are done):
In the triangle ABC M is the midpoint on AB. Let OA = $\vec{a}$, OC = $\vec{c}$ and OB = $\vec{b}$.
a) Find the vector OM expressed with $\vec{a}$ and $\vec{b}$.
b) The point P is on CM so that CP = 2PM. Find OP expressed with $\vec{a}, \vec{b}$ and $ \vec{c}$.
c) Let N be the midpoint on AC. The point Q is suppose to be on BN so that BQ = 2QN. Show that P = Q.
Logically, how does one go about doing this?
Would you assume that these points are not equal and try to derive a contradiction? Or would you make that point waypoint for another vector sum and show somehow that by implication they are indeed equal?
I know they are equal. In the head of the task the following definition is given; OA = $\vec{a}$, OC = $\vec{c}$ and OB = $\vec{b}$.