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The average angle difference due to rotation was 2533

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Unformatted text preview: ding angles at the two respectively. As a result, the average of the three angles was taken the angle difference of all three vectors. When the vector  ­square was rotated, we obtained different results for the angle, the x ­component, and the y ­component. However, the magnitude remained the same, it was just in a different direction. 9 2. Use the information you recorded to calculate the displacement vector between Origin 1 to Origin 2. The displacement vector between origin 1 and origin 2 was calculated using, the positions for each origin. Origin 1 was found to be at (0,0) and Origin 2 was at ( ­3.5,  ­4.5). The formula used to determine the displacement vector is: [(X1 ­X2)2 + (Y1 ­Y2)2]. This led us to the value of 5.7 cm as our displacement vector. See calculation details for reference. 3. Which aspects of the vectors change when the axes are rotated? Which aspects stay the same? Which aspects change when the origin is moved? Which stay the same? When axes are rotated the magnitude of the vector remains the same, but the direction changes. Furthermore, if the origin is moved and the axes are not changed, the magnitude of the vector changes and the direction of the vector changes. 4. Discuss the components of a vector. Are they unique? That is, can different sets of components represent the same vector? Is a set of components sufficient to describe a vector? In order to calculate the angle occurring when the vector  ­square is rotated (not when its origin is changed), the original angles of each of the three vectors were subtracted from each or their respective and correlating vector angles, which resulted when the vector ­square was rotated. The average angle difference due to rotation was 25.33 degrees for the three vectors. Upon rotation of the vector  ­ square, the x and y ­components all change, while the overall magnitude stays constant. These findings prove that differing sets of components can indeed represent the same vector. Hereafter, in order to sufficiently and accurately describe a vector, it is necessary to note the position and rotation of the coordinate system or systems in question. As far as whether t he components of a vector are unique, they are unique in the sense that while they are perpendicular to each other (and thus in this way similar), any increasing of or decreasing of one component does not and will not have a resultant effect on another com ponent. 5. For each of the coordinate systems used, determine the vectors R1 + R2 and R3 R1. What does this show you about the relationships between vectors and how they relate to different coordinate systems? By rotating the axes the coordinate system, the magnitude remains...
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