Algebra 2 Common Core

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

Chapter 12 - Matrices - 12-6 Vectors - Practice and Problem-Solving Exercises: 32

Answer

$$\langle2,-3\rangle$$

Work Step by Step

To scale a vector in component form, multiply each component by the scale factor. $$2\vec{u}=2\langle -5,3\rangle=\langle 2\times (-5),2\times 3\rangle=\langle-10,6\rangle.$$ $$3\vec{v}=3\langle 4,-3\rangle=\langle 3\times 4,3\times (-3)\rangle=\langle12,-9\rangle$$ To add vectors in component form, add x and y components separately. $$2\vec{u}+3\vec{v}=\langle -10,6\rangle+\langle 12,-9\rangle=\langle -10+12,6-9\rangle=\langle2,-3\rangle$$
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