Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.1 Vectors in the Plane - Exercises - Page 649: 3


See the figure below.

Work Step by Step

Assume that the terminal point of the vector $ a=\langle 1,3\rangle $, is $(x,y)$, then we have $$\langle 1,3\rangle =(x,y) - (2,2)\Longrightarrow x=3, \quad y=5$$ and hence $ a $ is based at $(2,2) $ and the terminal point at $(3,5)$. So, the equivalent vector to $ a $ and based at the origin is $\langle 1,3\rangle $ as in the following figure.
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