Position & Displacement Vectors Flashcards

All 5 cards in this deck

What is a position vector?

The vector from the origin $O$ to a point.

e.g. $A(3,5)$ has position vector $\begin{pmatrix}3\\5\end{pmatrix}$.

What does the notation $\overrightarrow{AB}$ mean?

The vector (displacement) from point $A$ to point $B$.

If $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$, what is $\overrightarrow{AB}$?

$\mathbf{b}-\mathbf{a}$ (end minus start).

True or false? $\overrightarrow{AB}=\overrightarrow{BA}$

False. $\overrightarrow{BA}=-\overrightarrow{AB}$ — same length, opposite direction.

What are the steps to find $\overrightarrow{PQ}$ from the coordinates of $P$ and $Q$?

e.g. $P(1,2)$ and $Q(4,7)$

1. Write the position vectors: $\mathbf{p}=\begin{pmatrix}1\\2\end{pmatrix}$, $\mathbf{q}=\begin{pmatrix}4\\7\end{pmatrix}$
2. Subtract: $\mathbf{q}-\mathbf{p}$
3. Answer: $\begin{pmatrix}3\\5\end{pmatrix}$