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Another example
Let's go back to our original equation
vecAC = vecAB + vecBC
and assume that the magnitude of vecAB is 30 and the magnitude of vecBC is 40. The sum of those two vectors (vecAC) can have a magnitude anywhere from 10 to 70depending on the relative angles of vecAB and vecBC.
A triangle with sides of 30, 4 0, and ?
The svg file for this exercise is named Phy1060c1.svg. The table of key-value pairs for this file is provided in Figure 5 .
| Figure 5 . Key-value pairs for the image in Phy1060c1.svg. |
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m: vecAC = vecAB + vecBC
n: Co: North
p: Resultant vector A Cq: Displacement vector B C
r: Displacement vector A Bs: A
t: Bu: File: Phy1060c1.svg
v: Eastw: 135 degrees |
The image contained in this file is shown in Figure 6 . A non-mirror-image version of the file is shown in Figure 16 .
| Figure 6 . Mirror image contained in the file named Phy1060c1.svg. |
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Graph board instructions
Go back to the graph board and change the direction of vecBC to northwest (135 degrees relative to the east-west horizontal line with east being zerodegrees) keeping the length at 40 meters.
What happened to the displacement?
Now what is the displacement of the point C relative to the point A? I can't do the arithmetic in my head for this problem, but I can measure the length ofvecAC to be about 28 meters and the angle of vecAC to be a little less than 90 degrees. (I will show you how to write a script to solve this problemmathematically later.)
Any number of displacements can be added
There is no limit to the number of displacement vectors that can be added in this manner. For example, pretend that you walk from point A,
Your displacement vecAG will be
vecAG = vecAB + vecBC + vecCD + vecDE + vecEF + vecFG
even if your zigzag path crosses back over itself one or more times.
Tactile graphics for the sum of six vectors
The svg file for this exercise is named Phy1060d1.svg. The table of key-value pairs for this file is provided in Figure 7 .
| Figure 7 . Key-value pairs for the image in Phy1060d1.svg. |
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m: A
n: Bo: C
p: Dq: E
r: Fs: G
t: The sum of six vectorsu: Not drawn to scale
v: Resultant vector A Gw: File: Phy1060d1.svg |
The image contained in this file is shown in Figure 8 . A non-mirror-image version of the file is shown in Figure 17 .
| Figure 8 . Mirror image contained in the file named Phy1060d1.svg. |
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Can be extended to three (or more) dimensions
The physics textbook titled College Physics by Mendenhall, Eve, Keys, and Sutton contains the following example.
"If a man climbs up the mast of a ship sailing east while the tide caries it south, then that sailor may have three displacements at right angles, vecAB30 feet upward, vecBC 100 feet eastward, vecCD 20 feet southward, all with respect to the bed of the ocean. The three displacements vecAB, vecBC, and vecCDare equivalent to the single displacement vecAD; and in the same way, any number of displacementsmay be added together."
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