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Addition of Vectors by Components
Every single vector can be resolved (broken down) into their component vectors. If we are dealing with a vector in the two dimensional plane, then we can break down the vector into two component vectors, which each lie along one dimension (the x and y axis). Likewise, if we are dealing with a vector in the three dimensional plane, we can resolve that vector into three component vectors. We usually use the xyz plane as the reference frame and begin our vector at the origin. Graphical methods of adding vectors can be very tedious and overall inefficient because they require of the use of protractors and rulers. A much more efficient method of adding or subtracting vectors used in physics and mathematics involves using component vectors. Suppose we want to add up two vectors to find the final resultant vector. First, we must break down each individual vector into its components. Next, we must add up the component vectors that lie along the same axis (for example, add up the all component vectors that lie along the x axis). Then we can use a formula as described in the lecture to find the magnitude as well as the direction of the resultant vector. This method provides us with an accurate and efficient way to determine the resultant vector without having to have to use precision instruments.
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