Consider a plane II whose unit normal vector pointing outward from the origin is n = ai+ bj+ck and the shortest distance from the origin O(0,0,0) is d, as shown in the figure. Show that all points P(x,y,z) on this plane satisfy the equation ax+ by+cz– d=0. •P d 1=

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.6: Equations Of Lines And Planes
Problem 2E
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Consider a plane II whose unit normal vector pointing outward from the origin is n = ai+
bj+ck and the shortest distance from the origin O(0,0,0) is d, as shown in the figure. Show
that all points P(x, y, z) on this plane satisfy the equation ax+by+cz–d=0.
п
•P
d
1=
Transcribed Image Text:Consider a plane II whose unit normal vector pointing outward from the origin is n = ai+ bj+ck and the shortest distance from the origin O(0,0,0) is d, as shown in the figure. Show that all points P(x, y, z) on this plane satisfy the equation ax+by+cz–d=0. п •P d 1=
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