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 756: 54

Answer

$$\mathbf{u}+\mathbf{v}=\left(5,\sqrt{3}\right)$$

Work Step by Step

$\|\mathbf{u}\|=4\hspace{5mm}\theta_u=0^\circ$ $\|\mathbf{v}\|=2\hspace{5mm}\theta_v=60^\circ$ $u_x=\|\mathbf{u}\|\cos{\theta_u}=4\cos{0}=4$ $u_y=\|\mathbf{u}\|\sin{\theta_u}=4\sin{0}=0$ $v_x=\|\mathbf{v}\|\cos{\theta_v}=2\cos{60}=2\frac{1}{2}=1$ $v_y=\|\mathbf{v}\|\sin{\theta_v}=2\sin{60}=2\frac{\sqrt{3}}{2}=\sqrt{3}$ Therefore, $\mathbf{u}+\mathbf{v}=\left(4+1,0+\sqrt{3}\right)$ $$\mathbf{u}+\mathbf{v}=\left(5,\sqrt{3}\right)$$
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