The Mission Tour: An Exercise in Vector Addition
Map or Poster Technique

Adding vectors using a ruler and a protractor:

If a poster of the area is available, it may be used to make measurements. The scale may be listed at the bottom of the poster or we will have to scale some known landmark in the image. The map used in the following example (almost any map will do) is a typical 'Road Atlas' with a scale of 2.0 centimeters = 20.0 miles. The locations in the story include the San Buenaventura Mission, the Santa Barbara Mission and the Santa Ines Mission which is located in Solvang.
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Mission locations:

  1. San Buenaventura Irrigation and climate would provide bountiful crops for this Mission. It is near modern day Highway 101.
  2. Santa Barbara Mission is located on a hill overlooking the City.
  3. Santa Ines Mission is near Highway 101 in the city of Solvang. Santa Ines was very remote and difficult to reach. Notice the mountain ranges in close proximity to the Mission.
 

 

Find the cities in which San Buenaventura, Santa Barbara, Santa Ines Missions reside.

Find each Mission on the map (or poster) and then simply measure from one location to another. Using the scale on your map, find the distances between each Mission. Convert centimeters to miles (or kilometers) using the scale for your map. If you have enough information to solve for the distances now, you may proceed. If not, click on 'Next'.

Use your protractor to measure appropriate angles to find the bearing for each vector. Remember that compass headings always begin at the 'North' line which is called 'Zero' degrees. This is not to be confused with the mathematician's "unit circle" which has "zero degrees" pointing to the right.

  Now, we can proceed to measure the legs of the journey, finding distance and bearing for each.

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