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Unformatted text preview: Notes for Unit : Introduction to Vectors Introduction to Vectors . What is a vector? A vector is a way of representing a straight line segment by describing the motion of the segment without reference to its speci c endpoints. Examp e Examp e Examp e : In the diagram shown on the le , point A is located at ( , ) , and point B is located at ( , ) . We can describe AB as a motion that travels- units in the x direction, and units in the y direction. We write, AB = - , . e arrow over AB indicates that the motion started at A and ended at B . Well use angle brackets to indicate the coordinates of a vector (although this notation is not universal). Examp e : In this example, AB = , , and CD = , also. ey are di erent line segments , but they represent the same motion , so they have the same vector coordinates. . Determining the coordinates of a vector If we know the points where a vector begins and ends, we can subtract the tail from the head to nd the coordinates of the vector: vector = head- tail Examp e : Point A is located at (- , ) and point B is located at ( , ) . Find the coordinates of AB . So ution: AB = B- A = ,- - , = ,- . Vector Addition and Sca ar Mu tip ication We can add and subtract vectors by adding and subtracting their individual components. We can also multiply a vectorWe can add and subtract vectors by adding and subtracting their individual components....
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This note was uploaded on 09/19/2011 for the course ENGE 1114 taught by Professor Twknott during the Fall '06 term at Virginia Tech.
- Fall '06