If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other. Find a, b and c.
If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other. Find a, b and c.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 21E
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If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other. Find a, b and c.
Expert Solution
Step 1
The parametric equation of the given line is
The general form of the parametric equation of a line is
Compare the given parametric equation with the general form, we get .
The equation of the given plane is .
The general form of the equation of a plane is .
Compare the equation of the given plane with general form and obtain .
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