Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
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Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 38

Answer

$(x,y,z) = (-3,-3,-6)$ $(x,y,z) = (3,3,6)$

Work Step by Step

$(x,y,z) = (0,0,0) + n(1,1,2) = (n, n, 2n)$ We can find the two values of $n$ such that the points on the line satisfy the equation of the sphere: $x^2+y^2+z^2 = 54$ $(n)^2+(n)^2+(2n)^2 = 54$ $ 6n^2 = 54$ $n^2 = 9$ $n^2-9 = 0$ $(n+3)(n-3) = 0$ $n=-3~~$ or $~~n=3$ We can find the two points: $(x,y,z) = (0,0,0) + (-3)(1,1,2) = (-3,-3,-6)$ $(x,y,z) = (0,0,0) + (3)(1,1,2) = (3,3,6)$
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