1.15: Past-paper question 8

Figure 2 shows triangle $\displaystyle AOB$

(a) (i) Find $\displaystyle \overrightarrow{AB}$ in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$

(ii) Find, in its simplest form, the exact value of $\displaystyle |\overrightarrow{AB}|$

(b) Find the area of triangle $\displaystyle AOB$

The point $\displaystyle C$ lies on $\displaystyle AB$ and $\displaystyle OD$ such that $\displaystyle O$, $\displaystyle C$ and $\displaystyle D$ are collinear.

(c) Use a vector method to find vector $\displaystyle \overrightarrow{OC}$ as a simplified expression in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$