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 - Page 814: 33



Work Step by Step

To scale a vector in component form, multiply each component by the scale factor. $$2\vec{v}=2\langle 4,-3\rangle=\langle 2\times 4,2\times (-3)\rangle=\langle8,-6\rangle$$ $$4\vec{w}=4\langle 2,2\rangle=\langle 4\times 2,4\times 2\rangle=\langle8,8\rangle$$ To subtract vectors in component form, subtract x and y components separately. $$2\vec{v}-4\vec{w}=\langle 8,-6\rangle-\langle 8,8\rangle=\langle 8-8,-6-8\rangle=\langle0,-14\rangle$$
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