Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 11 - Vectors and Vector-Valued Functions - 11.2 Vectors in Three Dimensions - 11.2 Exercises: 12

Answer

A: $(5,0,10)$ B: $(0,8,0)$ C: $(5,8,10)$

Work Step by Step

Given the two vertices, we find the maximum value for each coordinate is $x=5$, $y=8$, and $z=10$. A is on the $xz$-plane, so the $y$ coordinate is zero. Thus, A is at $(5,0,10)$. B is on the $yz$-plane and $xy$-plane, so the $x$ and $z$ coordinate is zero. Thus, B is at $(0,8,0)$. C is directly on top of the vertex $(5,8,0)$, meaning that only the $z$ coordinate is different. C is on the same plane as $(0,0,10)$, making the $z$ coordinate $10$. Thus, C is at $(5,8,10)$.
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