Vectors - Clemson University

A P P E N D I Scaling a Unit or Direction vector vector Points and Parametric definition of lines and Dot or inner Trigonometric interpretation of dot Geometric interpretation of dot Dot product example: The distance from a point to Dot product example: Mirror Cross Trigonometric interpretation of cross Cross product example: Finding surface Cross product example: Computing the area of Foundations of Physically Based Modeling and AnimationTo a mathematician, a vector is the fundamental element of what is known as a vectorspace, supporting the operations of scaling, by elements known as scalars, and alsosupporting addition between Vectors . When using Vectors to describe physical quantities,like velocity, acceleration, and force, we can move away from this abstract definition, andstick with a more concrete notion. We can view them as arrows in space, of a particularlength and denoting a particular direction, and we can think of the corresponding scalarsas simply the real numbers.

Algebraically, this is equivalent to adding corresponding terms of the two vectors: a + b = " a x a y # + " b x b y # = " a x + b x a y + b y #: We can think of this as again making a trip from the start of the first vector to the end of the second vector, but this time traveling first horizontally the distance a x + b x and then vertically the ...

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  Vector, Adding

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