2.7 Position Vectors Learning Goal: To find a position vector between two arbitrary points. As shown, two cables connect three points. C is below A by a distance C₂ = 1.50 ft and connected to A by a cable 12.1 ft long. Cable AC forms an angle B = 17.0° with the positive y axis. B is 7.90 ft above C and the distances B₂ and By are 7.10 ft and 4.70 ft, respectively. (Figure 1 ) Figure Part C - Position vector from A to C TAC = 1 of 1 The length of cable AC is 12.1 ft, and the cable forms the angle = 17.0° with the y axis. Given this information and the dimensions provided in the figure, find the position vector from A to C. Express the position vector in component form. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) ■VAΣo↓vec 3 1 ? ift, jft, k ft Part D - Position vector from B to C Find the position vector from B to C. Express your answer in component form. Express your answers, separated by commas, to three significant figures. ▸ View Available Hint(s) TBC == AΣ Ivec 6 Part E - Tension in the cable μA A cable is attached between B and C. The cable is attached in such a way that it has a tension of TBC along its length. The tensile force will attempt to pull B toward C. The force exerted on B has a z component with a magnitude of 10 lb. What is the magnitude of the tension in the cable, TBC? Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) TBC= Value Units ? ? ift, jft, k ft

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 16EQ

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Learning Goal:

To find a position vector between two arbitrary points.

As shown, two cables connect three points. C is below A by a distance Cz=1.50 ft=1.50 ft and connected to A by a cable 12.1 ft12.1 ft long. Cable AC forms an angle β=17.0∘=17.0∘ with the positive y axis. B is 7.90 ft7.90 ft above C and the distances Bx and By are 7.10 ft7.10 ft and 4.70 ft4.70 ft, respectively. (Figure 1)