Concept:
Vectors are mathematical objects for which an addition operation is defined. Geometrically, there are two popular ways to find the sum of two vectors, called the resultant: the Parallelogram method and the Tip-to-Tail method.
Vector Addition
Rectangular coordinates |
Polar coordinates |
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| x | y | r | θ° | |
vector A: |
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vector B: |
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A + B: |
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INSTRUCTIONS
Enter two vectors by clicking in the graph area, by typing numbers in the entry fields, or by using the sliders. When you select an addition method, the resultant vector and its coordinates will be displayed. After they are added, the vectors may be changed by dragging the tip of the arrows or any supplied drag points, or by deleting values in any of the available entry fields and entering new values. When the values are deleted, all entry fields for that vector will be ready for input.
EXPLORATIONS
Exploration 1:
How are the tip-to-tail method and the parallelogram method related?
Exploration 2:
Vector addition is commutative: for any two vectors A and B, A + B = B + A. Explain this property using the parallelogram method.
Exploration 3:
Vector addition is associative: for any three vectors A, B, and C, (A + B) + C = A + (B + C). For this reason, such a sum is usually written A + B + C. Explain how the sum A + B + C is found using the tip-to-tail method.
