Vector Arithmetic Playground

With Snap on, dragged tips snap to whole numbers.

• Draw. Each vector is drawn from the origin. The count to each tip is drawn as a dotted path: across by the first component, then up by the second component.
• Length. A right triangle is drawn under each vector. Show numbers works out the length $\lVert\overline{u}\rVert = \sqrt{u_1^2 + u_2^2}$.
• Sum. For $\overline{u} + \overline{v}$, $\overline{v}$ is redrawn dashed at the tip of $\overline{u}$. The sum is the heavy arrow. Parallelogram draws the other order as well. The tip is the same in both orders.
• Difference. $\overline{u} - \overline{v}$ is drawn as $\overline{u} + (-1)\overline{v}$, and the reversed arrow is labeled $(-1)\overline{v}$.
• Scalar multiple. $c\,\overline{u}$ is $\overline{u}$ scaled by the slider value $c$. A negative $c$ reverses the direction, and the length scales by $\lvert c\rvert$. A fraction such as 1/2 can be typed in the box.

A dashed arrow is always a vector redrawn away from the origin. Show R gives the Lesson 16 commands for the vectors on screen.

Under More:

• Third vector. A third vector $\overline{w}$ is added with either sign. With a third vector on, Sum and Difference draw all three tip to tail. When the example with $\overline{w}$ (Lesson 16 Example 2) is picked, More opens and the third vector is turned on.
• Base point. A copy of $\overline{u}$ is drawn from a base point dragged anywhere on the board (Lesson 15 Example 2).

Keys: press U, V or W to pick a tip, or B to pick the base point under More. Press an arrow key to move it one step of 1. With Snap off, the step is 0.1. Hold Shift with an arrow key to move it five steps.