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: 5

Answer

All three vectors have the same magnitude. The magnitude of a vector $\vec{v}=\langle v_x,v_y\rangle$ is $|\vec{v}|=\sqrt{v_x^2+v_y^2}.$ Therefore, $$|\langle 3,4\rangle|=\sqrt{3^2+4^2}=5$$ $$|\langle -4,3\rangle|=\sqrt{(-4)^2+3^2}=5$$ $$|\langle 4,-3\rangle|=\sqrt{4^2+(-3)^2}=5.$$

Work Step by Step

The magnitude of a vector $\vec{v}=\langle v_x,v_y\rangle$ is $|\vec{v}|=\sqrt{v_x^2+v_y^2}.$ Therefore, $$|\langle 3,4\rangle|=\sqrt{3^2+4^2}=5$$ $$|\langle -4,3\rangle|=\sqrt{(-4)^2+3^2}=5$$ $$|\langle 4,-3\rangle|=\sqrt{4^2+(-3)^2}=5.$$
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