6 (a) In the diagram below, OB = 4OA and AC = 5AX. M is the midpoint of BC, OA = a and BM = b. (i) Express in terms of a and/or b. (a) AB

here are the solutions to the questions.

6 (a) In the diagram below, $\vec{OB} = 4\vec{OA}$ and $\vec{AC} = 5\vec{AX}$. M is the midpoint of BC, $\vec{OA} = \vec{a}$ and $\vec{BM} = \vec{b}$.

(i) Express in terms of $\vec{a}$ and/or $\vec{b}$.

(a) $\vec{AB}$

Step 1: Use the vector addition rule $\vec{AB} = \vec{AO} + \vec{OB}$.
Given $\vec{OA} = \vec{a}$, so $\vec{AO} = -\