7.4. Find coordinates and vectors from a midpoint with position vectors
G7. Vectors in two dimensions

Question

The position vector of A, relative to O, is $\vec{OA}$ = $\begin{pmatrix} 3\\2\end{pmatrix}$ and the coordinates of B are (5, -10).

(a) Find the coordinates of C such that $\vec{OC} = 3\vec{OA} + \vec{OB}$ . [1]

(b) Given that D is the midpoint of AB, express $\vec{OD}$ as a column vector. [2]

Solution

In