Some properties of vectors - there is a point I don't understand it .

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Two vectors A and B are considered equal if they possess the same magnitude and direction, allowing for parallel translation in diagrams without altering their properties. An example provided is vector u, defined as i + j, and vector v, extending from (2, 1) to (3, 2), both having a magnitude of sqrt(2) and forming a 45-degree angle with the positive x-axis. This illustrates that vectors can be moved parallel to themselves while maintaining their characteristics. Understanding this property is crucial for visualizing and manipulating vectors in various applications. The discussion emphasizes the foundational concepts of vector equality and translation.
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Two vectors A and B are equal if they have the same magnitude and the same direction . this property allows us to translate a vector parallel to itself in a diagram without affecting the vector . In fact , for most purposes, any vector can be moved parallel to itself without being affected .



can you give me an example of that point
 
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Let u = i + j

Let v be the vector that extends from (2, 1) to (3, 2)

Then |u| = |v| = sqrt(2)
and both vectors make an angle of 45 degrees with the positive x-axis.
 
Thanks a lot
 
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