Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - Chapter Review Exercises - Page 701: 14


The length of $ v $ is $$\|v\|=\sqrt{26}\approx 5.1.$$ Also, we have $$2v+3(4i-k)=18i-2j+5k.$$ With length $\sqrt{353}\approx 18.8$

Work Step by Step

The length of $ v $ is given by $$\|v\|=\sqrt{9+1+16}=\sqrt{26}\approx 5.1.$$ Also, we have $$2v+3(4i-k)=6i-2j+8k+3(4i-k)=18i-2j+5k.$$ The length of this vector is: $\sqrt{18^2+(-2)^2+5^2}=\sqrt{18^2+4+25}=\sqrt{353}\approx 18.8$
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