Problem Solving with Vectors Flashcards

All 5 cards in this deck

If $M$ is the midpoint of $AB$, what is $\overrightarrow{AM}$ in terms of $\overrightarrow{AB}$?

$\frac{1}{2}\overrightarrow{AB}$

$M$ lies on $OR$ with $OM:MR=2:3$. What is $\overrightarrow{OM}$ in terms of $\overrightarrow{OR}$?

$\frac{2}{5}\overrightarrow{OR}$ — $M$ is 2 parts out of 5 along $OR$.

What are the steps to prove that points $A$, $B$ and $C$ are collinear (lie on a straight line)?

e.g. $\overrightarrow{AB}=3\mathbf{a}+4\mathbf{b}$, $\overrightarrow{AC}=15\mathbf{a}+20\mathbf{b}$

1. Write both vectors in terms of $\mathbf{a}$ and $\mathbf{b}$
2. Show one is a multiple of the other: $\overrightarrow{AC}=5\overrightarrow{AB}$
3. State they are parallel and share the point $A$, so $A$, $B$, $C$ are collinear

True or false? Showing that $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are multiples of each other proves $A$, $B$, $C$ and $D$ lie on a straight line.

False. It only proves the lines are parallel; collinearity also needs a common point.

$D$, $E$, $F$ are on a straight line and $\overrightarrow{DF}=-2.5\overrightarrow{DE}$. What is the ratio of lengths $DF:DE$?

$5:2$ — use the size of the scalar and ignore its sign.