The opposite direction magnitude of a vector the

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the opposite direction: Magnitude of a Vector: The Magnitude of a vector is also known as the “length” or “norm” of a vector. For vectors in R 3 , this is given by the Pythagorean Theorem: 2 2 2 z y x a a a a Unit Vectors:
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A unit vector is a vector with a magnitude of one (that is, a vector with “unit length.”) A unit vector is often (but not always) denoted with a “hat” instead of an arrow. Unit vectors can be used to signify a direction. Given a vector ) , , ( z y x a a a a , we can find a unit vector that points in the same direction as a : 2 2 2 2 2 2 2 2 2 2 2 2 , , ) , , ( | | ˆ z y x z z y x y z y x x z y x z y x a a a a a a a a a a a a a a a a a a a a a We can compactly express the magnitude and direction of a vector by using the unit vector: a a a ˆ | | This reads: “the vector a has a magnitude | | a and points in the direction a ˆ .” Physics notation: We will use a (no arrow, plain type) instead of | | a . e.g. a a a ˆ A Very Special Unit Vector: The position vector ) , , ( z y x r is a vector from the origin to an arbitrary point in R 3 . The magnitude of the position vector is the distance from the origin to ( x,y,z) .
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