Calculus 8th Edition

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

Chapter 12 - Vectors and the Geometry of Space - 12.3 The Dot Product - 12.3 Exercises - Page 853: 28


$ \lt -0.39282 , 0.919615\gt and \lt 0.99282,-0.119615 \gt$

Work Step by Step

Two unit vectors that make an angle of $60^\circ$ with $v= \lt 3,4 \gt$ $x^2+y^2=1$ $x^2+((1/8)(5-6x))^2=1$ $100x^2-60x-39=0$ $x= \dfrac{3 \pm 4 \sqrt 3}{10} \approx -0.39282,0.99282$ and $y=(1/8)(5-6x)\approx (1/8)(5-6(-0.39282))\approx 0.919615$ $y=(1/8)(5-6x)\approx (1/8)(5-6(0.99282))\approx -0.119615$ Hence, the two unit vectors are: $ \lt -0.39282 , 0.919615\gt and \lt 0.99282,-0.119615 \gt$
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