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# Adding Vectors for AP Physics B & C

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By McGraw-Hill Professional
Updated on Feb 10, 2011

Practice problems for these concepts can be found at: Vectors Practice Problems for AP Physics B & C

Let's take two vectors, Q and Z, as shown in Figure 9.3a.

Now, in Figure 9.3b, we place them on a coordinate plane. We will move them around so that they line up head-to-tail.

If you place your finger at the origin and follow the arrows, you will end up at the head of vector Z. The vector sum of Q and Z is the vector that starts at the origin and ends at the head of vector Z. This is shown in Figure 9.3c.

Physicists call the vector sum the "resultant vector." Usually, we prefer to call it "the resultant" or, as in our diagram, "R."

### Vector Components, Revisited

Breaking a vector into its components will make many problems simpler. Here's an example:

To add the vectors in Figure 9.4a, all you have to do is add their x- and y-components. The sum of the x-components is 3 + (–2) = 1 units. The sum of the y-components is 1 + 2 = 3 units. The resultant vector, therefore, has an x-component of +1 units and a y-component of +3 units. See Figure 9.4b.

### Some Hints

1. Make sure your calculator is set to DEGREES, not radians.
2. Always use units. Always. We mean it. Always.

Practice problems for these concepts can be found at: Vectors Practice Problems for AP Physics

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