Consider the planes 1x + 5y + 3x = 1 and 1x + 3z = 0. (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with positive first coordinate that is parallel to both planes. u i+ + k (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes. r(t) =i+j+k

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Consider the planes 1x + 5y + 3z = 1 and 1x + 3z = 0.
(A) Find the unique point P on the y-axis which is on both planes.
(B) Find a unit vector u with positive first coordinate that is parallel to both planes.
u=
+0j
i+
+
(C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes.
r(t) = ■ i-
k
Transcribed Image Text:Consider the planes 1x + 5y + 3z = 1 and 1x + 3z = 0. (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with positive first coordinate that is parallel to both planes. u= +0j i+ + (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes. r(t) = ■ i- k
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