Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 11 - Vectors and the Geometry of Space - 11.1 Exercises - Page 755: 35

Answer

$(\frac{1}{\sqrt{17}},\frac{4}{\sqrt{17}})$

Work Step by Step

The unit vector in the direction of v is $ v/||v|| = (v_1,v_2)/||(v_1,v_2)|| = $$(3,12)/\sqrt{3^2+12^2}$ =$(\frac{3}{\sqrt{153}},\frac{12}{\sqrt{153}})$ = $(\frac{3}{3\sqrt{17}},\frac{12}{3\sqrt{17}}) = (\frac{1}{\sqrt{17}},\frac{4}{\sqrt{17}})$ , which is of length one from definition of unit vector.
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