Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 3 - Vectors - Problems - Page 57: 11c


$\approx 132^0$

Work Step by Step

Sum of two vectors can be written as $\overrightarrow {r}=\overrightarrow {a}+\overrightarrow {b}$ $r=(a_{x}\widehat {i}+a_{y}\widehat {j}+a_{z}\widehat {k})+(b_{x}\widehat {i}+b_y\widehat {j}+b_{z}\widehat {k}) =\left( a_x+b_x\right) \widehat {i}+\left( a_y+b_y\right) \widehat {j}+\left( a_{z}+b_{z}\right) \widehat {k}=\left( 4.0m+\left( -13.0m\right) \right) \widehat {i}+\left( 3.0m+7.0m\right) \widehat {j}=-9.0m\widehat {i}+10.0m\widehat {j}$ Then the angle of this vector can be calculated using, $\tan \theta =\dfrac {r_y}{r_x}=\dfrac {10.0m}{-9.0m}=-\dfrac {10}{9}\Rightarrow \theta =\tan ^{-1}\left( -\dfrac {10}{9}\right) \approx 132^0$
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