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He had left his home in in Shasta County, California, on Thursday to go to the doctor, he told CNN on Sunday. The Carr Fire had been burning for four days at that point and Bledsoe said he didn’t realize the fire was coming into his neighborhood.

He also said his family was never told to evacuate.

While he was out, his 70-year-old wife, Melody Bledsoe, called and told him she could see the fire and that he needed to come get her and their great-grandchildren, 4-year-old Emily Roberts and 5-year-old James Roberts, who Ed Bledsoe called “Junior.”'

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Figure 1.1.1 – Graphical Vector Addition
Figure 1.1.2 – Vector Addition is Commutative
What about subtracting two vectors? Well, we can do this by following the same method as for regular numbers: Whichever vector we wish to subtract we multiply by –1, and then add the result to the other vector, which we do in the manner described above. We already know that multiplying a vector by –1 reverses its direction (and leaves its magnitude unchanged), so this is a well-defined operation for us.
Vector Components
The graphical method of adding vectors are not always convenient. For example, we shouldn’t have to actually measure the length of the new vector, we should be able to calculate it. Well, of course we can do this using some sophisticated knowledge of triangles. For example, given we know the lengths and directions of the two vectors we are adding, we can determine the length of the third leg of the triangle using the Law of Cosines:
\[ C^2 = A^2 + B^2 -2AB \cos \theta\]
With all of the lengths of the triangle legs and one of the angles (the one between \(A\) and \(B\)), we can get the other angles using the Law of Sines.
Exercise
The magnitudes of the two vectors shown in the diagram below are: \(A=132\) and \(B=145\). Find the magnitude and direction (angle made with the \(x\)-axis) of the vector that is the difference of these two vectors.
Solution
While we can use these tools to mathematically solve for the sum of two vectors, it turns out that there is another way we can do it that doesn’t require quite as much geometrical reasoning. This method exploits three simple facts:
We can replace any single vector as a sum of two (or more) vectors.
It is easy to add two vectors that are parallel.
If we use right triangles, trigonometry is easier to work with than with general triangles and the law of cosines/sines.
The trick is to select two (or three, if necessary) perpendicular axes (they do not have to be horizontal and vertical, they only need to be perpendicular to each other), and break up every vector involved into a sum of two perpendicular vectors parallel to these axes. The lengths of these perpendicular vectors are called the components of the vector along those axes. Going back to the list of advantages above, remember that we can add similar components like numbers, and we can determine these components easily using trigonometry.
Figure 1.1.3 – Vector Components
Figure 1.1.4 – Summing Vectors Using Components
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