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 58: 27a

Answer

$d_{1}$ = 8i + 16j

Work Step by Step

$d_{1}$ + $d_{2}$ = 5$d_{3}$ $d_{1}$ - $d_{2}$ = 3$d_{3}$ $d_{3}$ = 2i + 4j Solve by substitution $d_{1}$ + $d_{2}$ = 5$d_{3}$ $d_{2}$ = 5$d_{3}$ - $d_{1}$ Now substitute the $d_{2}$ from above into the second given equation of $d_{1}$ - $d_{2}$ = 3$d_{3}$ Which gives you... $d_{1}$ - 5$d_{3}$ + $d_{1}$ = 3$d_{3}$ Which reduces to 2$d_{1}$ = 8$d_{3}$ Which gives us $d_{1}$ = 4$d_{3}$ Now we have to substitute in the third given equation of $d_{3}$ = 2i + 4j, so that $d_{1}$ will be in unit vector notation. Thus... $d_{1}$ = 8i + 16j
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