Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 12 - Matrices - 12-6 Vectors - Lesson Check: 3

Answer

$$\langle-1,-12\rangle$$

Work Step by Step

$\vec{RS}$ is the vector from point $R:(-2,5)$ to $S:(2,-8).$ The change in the x-direction is $$2-(-2)=4.$$ The change in the y-direction is $$-8-5=-13.$$ So the vector can be written in component form as $$\vec{RS}=\langle4,-13\rangle.$$ $\vec{RQ}$ is the vector from point $R:(-2,5)$ to $Q:(3,4).$ The change in the x-direction is $$3-(-2)=5.$$ The change in the y-direction is $$4-5=-1.$$ So the vector can be written in component form as $$\vec{RQ}=\langle5,-1\rangle.$$ To get the difference of two vectors, subtract components. $$\vec{RS}-\vec{RQ}=\langle4,-13\rangle-\langle5,-1\rangle=\langle-1,-12\rangle$$
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