Calculus (3rd Edition)

Published by W. H. Freeman

Chapter 13 - Vector Geometry - 13.1 Vectors in the Plane - Exercises - Page 650: 32

Answer

Since $\overrightarrow {AB}$ and $\overrightarrow {PQ}$ have the same components, they are equivalent.

Work Step by Step

We have $A = \left( {5,8} \right)$ and $B = \left( {1,8} \right)$. So, $\overrightarrow {AB} = \left( {1,8} \right) - \left( {5,8} \right) = \left( { - 4,0} \right)$. We have $P = \left( {1,8} \right)$ and $Q = \left( { - 3,8} \right)$. So, $\overrightarrow {PQ} = \left( { - 3,8} \right) - \left( {1,8} \right) = \left( { - 4,0} \right)$. Since $\overrightarrow {AB}$ and $\overrightarrow {PQ}$ have the same components, they are equivalent.

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