How is the magnitude of related to its scalar components

Chapter 1, Problem 1.17

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How is the magnitude of related to its scalar components Ax and Ay? Answer The magnitude of is given by the Pythagorean theorem in the form , since a vector and its components form a right triangle (see Figure 1.26). Do any of the vectors in Figure 1.25 have a zero value for either their x or y components? Answer Yes. The vectors and each have a zero value for their y component. This is because these vectors are parallel to the x axis. What does the fact that , , and add together to give the resultant tell you about the components of these vectors? Answer The fact that means that the sum of the x components of , , and equals the x component of (Ax Bx Cx Rx) and the sum of the y components of , , and equals the y component of (Ay By Cy Ry). Solut