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: 35

Answer

$$\langle18,-13\rangle$$

Work Step by Step

To scale a vector in component form, multiply each component by the scale factor. $$-3\vec{u}=-3\langle -5,3\rangle=\langle (-3)\times (-5),(-3)\times 3\rangle=\langle15,-9\rangle$$ $$-\frac{1}{2}\vec{w}=-\frac{1}{2}\langle 2,2\rangle=\langle (-\frac{1}{2})\times 2,(-\frac{1}{2})\times2\rangle=\langle-1,-1\rangle$$ To add vectors in component form, add x and y components separately. $$-3\vec{u}+\vec{v}-\frac{1}{2}\vec{w}=\langle 15,-9\rangle+\langle 4,-3\rangle+\langle-1,-1\rangle=\langle 15+4-1,-9-3-1\rangle=\langle18,-13\rangle$$
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