MATH 32A Lecture Notes - Lecture 2: Unit Vector, Square Root, Linear Combination
Document Summary
Lecture 2 notes: unit vectors, vectors in 3-d. A vector is a directed line segment, or an object with size and direction. Usually drawn as an arrow, the starting point of arrow is called the initial point and the tip of the arrow is called the terminal point. Length of a vector if v = : ||v|| = square root of (a 2 + b 2 ). A scalar is a real number that does not have direction, only magnitude. Unit vector: scaling a vector down to unit length. This is because by definition, length of unit vector is 1. Thus, multiplying the length of the vector by the scalar above will yield a vector with the same direction but with length 1. Because components of vector and length of vector are equal because they both describe the same vector, components of unit vector is (1/||v||) (v).
