MAT 21C Lecture Notes - Lecture 12: Scalar Multiplication, Unit Vector, Cartesian Coordinate System
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MAT 21C Full Course Notes
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Announcements: o ce hours f 10/21 1-2 msb 3106. A point p in 3-dimensional space written in cartesian coordinates is p (x, y, z). A directed line segment is called a vector. A vector ~v from point a to b is written ~v = The distance between p1(x1, y1, z1) and p2(x2, y2, z2) is. The length or magnitude of a vector ~v is denoted | A vector ~v of length one is called a unit vector. | ~v | is a unit vector called the direction of ~v . Let ~u = hu1, u2, u3i and ~v = hv1, v2, v3i be two vectors and s a scalar. Addition: ~u + ~v = hu1 + v1, u2 + v2, u3 + v3i. Scalar multiplication: s ~u = hsu1, su2, su3i. Dot product: ~u ~v = u1v1 + u2v2 + u3v3. Cross product: ~u ~v = h i.