MATH 1152 Chapter Notes - Chapter 12: Parallelogram, Cross Product, Scalar Multiplication
12 Dec 2016
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Document Summary
Vectors are quantities that have both length and direction. Two vectors are equal if they have the same length and direction. We define the zero vector to be the vector with length 0 and no direction. (cid:3017)(cid:3018) : the zero vector is denoted. A vector may be denoted (cid:3017)(cid:3018) = (cid:2868) . A vector beginning at the origin is called a position vector. There is a difference between (1,3) and <1,3> Scalar multiplication: scalar is another word for a real number (to distinguish from vectors) Scalar multiplication is an operation that takes a scalar c and a vector vector denoted. The length or magnitude of a vector (cid:3049) (cid:3049) = is given by | | <1,3> | = (cid:883)+9= (cid:883)(cid:882) (cid:3049) = c (cid:3048) for some scalar c. if c > 0 (cid:3049) are parallel if (cid:3048) and (cid:3049) have opposite direction (cid:3048) and (cid:3049) be a nonzero vector.
