vector - Vectors Everywhere more than just the usual,...

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1 Vectors Geometry & Algebra of Vectors; Scalar and Cross Products Vectors Everywhere more than just the usual, familiar “magnitude and irection” business direction business well-known applications: e.g. wind velocity not-so-well-known applications: computer science (codes: ISBN, UPC, etc.) statistics economics life & social sciences Geometric Vectors Vectors are represented geometrically as directed e segments or arrows in 2- ace or 3- ace. line segments or arrows in 2 space or 3 space. The direction of the arrow specifies the direction of the vector, and the length of the arrow describes its magnitude. We denote vectors in lowercase boldface type and refer to numbers as scalars denoted in lowercase italics Equivalent Vectors If the initial point of a vector v is A and the terminal point is B , we write Vectors with the same length and same direction, are equivalent . Equivalent vectors are regarded as equal even though they may be located v = AB q gy y in different positions. If and w are equivalent, we write v = w
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2 Vector Addition If v and w are any two vectors, then the sum v + w is the vector determined as follows: Position the vector so that its initial point coincides with the terminal point of v (head he vector is to tail) . The vector is represented by the arrow from the initial point of to the terminal point of The zero & negative vector The vector of length zero is called the zero nd is denoted by We define vector and is denoted by 0 . We define v + 0 = v for every vector . If is any nonzero vector, then , the negative of , is defined to be the vector that has the same magnitude as but is ppositely directed oppositely directed v + (- v )= 0 Vector arithmetic v - w = v +(- w ) Vector subtraction is addition of negative Scalar multiple of vector: k v is the vector in the same direction as v but k times as long Summary: Arithmetic Properties of Vectors
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3 Vectors in coordinate systems Problems involving vectors can often be simplified y introducing a rectangular (Cartesian) coordinate
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vector - Vectors Everywhere more than just the usual,...

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