MYP Extended Mathematics Vector Representation Questionbank

In a parallelogram $ABCD$, the position vectors of three vertices relative to an origin $O$ are $\overrightarrow{OA} = \mathbf{a}$, $\overrightarrow{OB} = \mathbf{b}$, and $\overrightarrow{OC} = \mathbf{c}$. Find the position vector of the fourth vertex, $\overrightarrow{OD}$.

A drone moves from a starting point $O$ with an initial translation $\mathbf{d}_1 = 4\mathbf{i} - 3\mathbf{j}$ and then follows with a second translation $\mathbf{d}_2 = -2\mathbf{i} + 5\mathbf{j}$. What is the total displacement from the start?

True or False: If the position vectors of points $P$ and $Q$ are $\mathbf{p}$ and $\mathbf{q}$ respectively, then the displacement vector $\overrightarrow{PQ}$ is calculated as $\mathbf{p} - \mathbf{q}$.

Which of the following expressions correctly represents the vector journey $\overrightarrow{DC}$ by going through point $B$?

True or False: If the vector $\mathbf{v} = 2\mathbf{i} - 5\mathbf{j}$ represents a translation, then the vector $-\mathbf{v}$ represents a translation of 2 units to the left and 5 units up.