advertisement

Section 9.1: Vectors in the Plane A vector in R2 has two components. It expresses magnitude and direction. Imagine an arrow with terminal and initial points. The vector from (1,2) to (4,8) is < 3, 6 > It can also be written 3i + 6j (4,8) (1,2) A “regular old number” is called a scalar. We can add vectors and multiply by scalars. 3, 6 5, 7 2, 13 (3i + 6j ) - (5i - 7j) = -2i + 13j 4 3, 6 12, 24 The norm of a vector is its length. || 3, 6 || 3 6 2 2 45 A unit vector has length 1. 3 6 , 45 45 is a unit vector in same direction as 3, 6 In a scene from Muppet Treasure Island, Clueless Morgan & Polly Lobster pull Gonzo’s arms with a force of <3, 6> N and <5, -9> N, respectively. The force on Gonzo is <3, 6> + <5, -9> = <8, -3> N