Vectors with MS Word

Vectors with MS Word M.C. Simani, 2007

This note takes example from the work of Rauben [Rauben, 2005] and other studies in science education related to students understanding of the concept of vector. Microsoft Word allows the creation and manipulation of vectors by using its drawing package. With this simple method it is possible to create hands-on exercises that help the visualization of vectors and the practicing of operations with vectors. Both qualitative and quantitative analyses are possible.

Activating the MS Word “Drawing” package On the “Tool” menu, choose “Customize” and make sure that “Drawing” is checked. You might already see the full “Drawing” toolbar at the bottom of the Word window. A vector can be created by selecting the “Arrow” icon on the Drawing toolbar.

Example of arrow-vector:

Examples of activities:

Step 1: practice drawing vectors using “Arrow”. Use “Copy” and “Paste” to create equivalent vectors.

Step 2: practice vector addition using the “head-to-tail” method: A + B = C

The component of any vector can be obtained by right-clicking on the arrow of interest and choosing “Format AutoShape”. The vector components are given as “height” and “width”. Also, you can specify a vector in terms of its magnitude and direction using “Format AutoShape”. First draw an horizontal vector, then select its “width” and “angle”. The “sign” of the vector can be specified by using the flip feature in the “Draw” menu. Note: MS Word uses a clock-wise sign convention.

In the example above, the components are as follow:

A: x=1.43”, y= 0.75”

B: x = 2.75”, y=0.5”

C: x = 1.38”+2.75”=4.13”, y=0.88”-0.5”=0.38”

Note that the correct sign has to be applied in order to find the correct y component for the vector C.

Translation of vectors It is important to notice that vectors created with MS word can be easily translated on the page without changing the characteristics of the vector. Operations such as multiplication and inversion can also be represented in an intuitive way. This hands-on minds-on process helps to build the appropriate cognitive concept of free vector. In particular, every translation of a vector represents itself a vector displacement from the initial position to the final position. Moreover, this translation could be performed in several ways as illustrated below: either a single shift (right figure) or multiple shifts (left figure).

Despite the difference in the procedure of translating the red vector, they both have the same final effect. That is, it does not matter how translation occurs, all that matters is the initial and final positions [Watson, 2002]. Some examples of tests with vectors [Nguyen, 2003]

1. Group together vectors that have the same magnitude.

2. Group together vectors that have the same direction.

3. Draw the resultant vector of A + B.

References [Rauben, 2005] Adding Vectors with Microsoft Word. J. Rauben, The Physics Teacher, (43) 2005.

[Watson, 2002] The relationship between physical embodiment and mathematical symbolism: the concept of vector. A. Watson et al. , 2002.

[Nguyen 2003] Initial understanding of vector concepts among students in introductory physics courses. N.L. Nguyen and D.E. Meltzer, American J. Physics (6), 2003.

Other Resources

Vectors Primer Resource Pages http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html