Representing Vectors as Diagrams Flashcards

All 4 cards in this deck

What are the steps to draw $\mathbf{a}+\mathbf{b}$ on a grid?

e.g. $\mathbf{a}=\begin{pmatrix}3\\2\end{pmatrix}$, $\mathbf{b}=\begin{pmatrix}-1\\4\end{pmatrix}$

1. Draw $\mathbf{a}$: 3 right, 2 up
2. From the tip of $\mathbf{a}$, draw $\mathbf{b}$: 1 left, 4 up
3. Draw the resultant from the start of $\mathbf{a}$ to the end of $\mathbf{b}$: $\begin{pmatrix}2\\6\end{pmatrix}$

What must a vector drawn on a grid always show?

An arrow giving its direction (plus its label if asked for).

How do you draw $-2\mathbf{a}$ given $\mathbf{a}$ on a grid?

e.g. $\mathbf{a}=\begin{pmatrix}1\\3\end{pmatrix}$

Twice as long as $\mathbf{a}$ and in the opposite direction.

e.g. draw $\begin{pmatrix}-2\\-6\end{pmatrix}$

On a diagram, what path represents $\mathbf{a}-\mathbf{b}$?

Travel along $\mathbf{a}$, then along $\mathbf{b}$ backwards (against its arrow).