Finding Vector Paths Flashcards

All 5 cards in this deck

What are the steps to express a vector such as $\overrightarrow{FE}$ in terms of $\mathbf{a}$ and $\mathbf{b}$?

e.g. $\overrightarrow{FC}=\mathbf{a}$, $\overrightarrow{CD}=-\mathbf{b}$, $\overrightarrow{DE}=\mathbf{a}+\mathbf{b}$

1. Find a route from $F$ to $E$ along known vectors: $F\to C\to D\to E$
2. Add them in order, using $-$ for any travelled backwards: $\mathbf{a}-\mathbf{b}+\mathbf{a}+\mathbf{b}$
3. Simplify: $2\mathbf{a}$

What does the triangle law give for $\overrightarrow{PQ}+\overrightarrow{QR}$?

$\overrightarrow{PR}$

In parallelogram $OABC$ with $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OC}=\mathbf{c}$, what is $\overrightarrow{AB}$?

$\mathbf{c}$ — opposite sides of a parallelogram are equal vectors.

True or false? Two different routes between the same two points give different vector expressions.

False. Every route simplifies to the same vector.

What does 'give your answer in its simplest form' mean for a vector expression?

Collect like terms in $\mathbf{a}$ and $\mathbf{b}$.

e.g. $\mathbf{a}-\mathbf{b}+\mathbf{a}+\mathbf{b}=2\mathbf{a}$