vectors - ectors The word vector comes from the Latin word...

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ectors The word vector comes from the Latin word vectus which means “carried”. It is best to think of a vector as the displacement from an initial point P to a terminal point Q . Such a vector is expressed as . The figure below shows a typical vector. Notice that the vector appears as a line with an arrow at one end. This is referred to as a directed line segment. The end with the arrow is the head of the vector, or the terminal point, while the other end is the starting, or initial point. PQ  Vectors have two important aspects: direction and magnitude. The direction tells you where to point the vector and the magnitude tells you how far to go in that direction. The magnitude of the vector PQ is written as PQ . Note that while this looks just like we take the absolute value of the vector , it means the distance between points P and Q . And so, to compute the magnitude of a vector, we use the distance formula. We use two different formulas, depending on whether or not the vector is in two dimensions or three dimensions. PQ P Q If our points are in two dimensions, then P can be expressed as ( p 1 , p 2 ) and Q can be expressed as ( q 1 , q 2 ). We have that PQ can be written as 11 2 2 , qp  and 22 () ( PQ q p q p  ) 1 . It helps to think of the magnitude of a vector as the hypotenuse of a triangle. Let us consider the above vector placed on the coordinate axes. Notice that the “base” of the triangle (which also happens to be parallel to the x -axis) is 1 while the “height” of the triangle (parallel to the y -axis) is 2 q P Q p 1 q 1 2 2 2 p . To find the length of the hypotenuse, we would square the two sides, add them together, and take the square root, just as we did above.
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This note was uploaded on 09/07/2011 for the course MATH 10C taught by Professor Hohnhold during the Spring '07 term at UCSD.

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vectors - ectors The word vector comes from the Latin word...

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