Representing Vectors as Diagrams Flashcards

All 6 cards in this deck

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

The vector of the journey from point $A$ to point $B$.

How do you draw a given column vector on a grid, starting from a point $P$?

e.g. draw $\begin{pmatrix}4\\-1\end{pmatrix}$ from $P$

Count the top number across and the bottom number up/down from $P$, then draw an arrow from $P$ to that point.

e.g. 4 right and 1 down from $P$, arrow pointing away from $P$.

On a diagram, how does $-\mathbf{a}$ compare with $\mathbf{a}$?

Same length and parallel, but the arrow points in the opposite direction.

On a diagram, how does $2\mathbf{d}$ compare with $\mathbf{d}$?

Twice as long, in the same direction.

True or false? Two arrows drawn in different places on a grid can represent the same vector.

True. If they have the same length and the same direction they are the same vector, wherever they are drawn.

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

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

1. Draw $\mathbf{a}$ from the starting point: 2 right, 1 up
2. Draw $\mathbf{b}$ starting at the tip of $\mathbf{a}$: 1 right, 3 up
3. Draw and label $\mathbf{a}+\mathbf{b}$ as the arrow from the start to the final point: $\begin{pmatrix}3\\4\end{pmatrix}$