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Calculating a resultant vector (or vector addition) is the reverse of breaking the resultant down into its components. If the perpendicular components A x A x and A y A y of a vector A A are known, then we can find A A analytically.
The three main methods for adding vectors are the polygon method, the parallelogram method and vector addition using its components. Here, we will look at some examples with answers and practice problems for the topic of vector addition.
Vectors can be added by using the polygon law irrespective of their number and sequence. Proof of the law of polygon of vectors: Let the magnitudes and directions of the vectors \(\vec{a}\), \(\vec{b}\), \(\vec{c}\), \(\vec{d}\) be represented, by the arms of the polygon OABCD, taken in order: \(\overrightarrow{O A}\), \(\overrightarrow{A B ...
Using the Graphical Method of Vector Addition and Subtraction to Solve Physics Problems Now that we have the skills to work with vectors in two dimensions, we can apply vector addition to graphically determine the resultant vector , which represents the total force.
By the end of this section, you will be able to: Understand the rules of vector addition and subtraction using analytical methods. Apply analytical methods to determine vertical and horizontal component vectors. Apply analytical methods to determine the magnitude and direction of a resultant vector.
The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other. The method is not applicable for adding more than two vectors or for adding vectors that are not at 90-degrees to each other.
Polygon Law of Vector. According to the polygon law of vector addition, if the number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented by magnitude and direction such that the closing side of the polygon is taken in the opposite direction.
