Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.4 - Vectors and Dot Products - 8.4 Exercises - Page 597: 92


If $u$ and $v$ are the diagonals of a rhombus, then $u\cdot v=0$

Work Step by Step

A rhombus can be formed by joining the points $(-a,0),(0,b),(a,0),(0,-b)$ The vectors from $(-a,0)$ to $(a,0)$ and from $(0,-b)$ to $(0,b)$ are the diagonals. The vector from $(-a,0)$ to $(a,0)$: $u=[a-(-a)]i+(0-0)j=2a~i$ The vector from $(0,-b)$ to $(0,b)$: $v=(0-0)i+[b-(-b)]j=2b~j$ $u\cdot v=2a~i\cdot 2b~j=0$ Hence, $u$ and $v$ are perpendicular.
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