Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.2 Vectors - 12.2 Exercises - Page 845: 7


$c=\frac{1}{2}a+\frac{1}{2}b$, $d=\frac{1}{2}b-\frac{1}{2}a$

Work Step by Step

As per parallelogram law: $a+b=2c$ Divide both sides by scalar $2$, we get $c=\frac{a+b}{2}$ $c=\frac{1}{2}a+\frac{1}{2}b$ From the figure we can see that: $a+2d=b$ $2d=b-a$ Divide both sides by scalar $2$, we get $d=\frac{b-a}{2}$ $d=\frac{1}{2}b-\frac{1}{2}a$
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