Splet1.2 Bases and Components of a Vector Addition and scalar multiplication of vectors allow us to de ne the concepts of linear combination, basis, components and dimension. These concepts apply to any vector space. A linear combination of vectors~a and~b is an expression of the form ~a+ ~b. This linear combination SpletDefinition 13.2 We let I represent the vector from the origin to the point (1,0), and J the vector from the origin to the point (0,1). These are the basic unit vectors (a unit vector is a vector of length 1). The unit vector in the direction θis cosθI + sinθJ. If V is a vector of length r and angle θ, then V = r (cosθI + cosθJ)
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