Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 9 - Section 9.1 - Vectors in Two Dimensions - 9.1 Exercises - Page 637: 35

Answer

$2\vec{u}=4\vec{i}$ $-3\vec{v}=-9\vec{i}+6\vec{j}$ $\vec{u}+\vec{v}=5\vec{i}-2\vec{j}$ $3\vec{u}-4\vec{v}=-6\vec{i}+8\vec{j}$

Work Step by Step

$\vec{u}=2\vec{i},$ $\vec{v}=3\vec{i}-2\vec{j}$ $2\vec{u}$ Multiply both components of $\vec{u}$ by $2$: $2\vec{u}=2(2\vec{i})=4\vec{i}$ $-3\vec{v}$ Multiply both components of $\vec{v}$ by $-3$ $-3\vec{v}=-3(3\vec{i}-2\vec{j})=-9\vec{i}+6\vec{j}$ $\vec{u}+\vec{v}$ Add the same component from both vectors together and simplify: $\vec{u}+\vec{v}=(2\vec{i})+(3\vec{i}-2\vec{j})=(2+3)\vec{i}-2\vec{j}=5\vec{i}-2\vec{j}$ $3\vec{u}-4\vec{v}$ Multiply $\vec{u}$ by $3$ and $\vec{v}$ by $-4$, then add the two vectors together and simplify: $3\vec{u}-4\vec{v}=3(2\vec{i})-4(3\vec{i}-2\vec{j})=(6\vec{i})+(-12\vec{i}+8\vec{j})=...$ $...=(6-12)\vec{i}+8\vec{j}=-6\vec{i}+8\vec{j}$
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