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July 5, 2015

Homework Help: Math: Intersections of 3 Planes

Posted by Anonymous on Thursday, March 27, 2008 at 9:41pm.

For what value of "k" will the following set of planes intersect in a line?

x - 2y - z = 0
x + 9y - 5z = 0
kx - y + z = 0


Work:

Elimination to find "z":
x - 2y - z = 0
x + 9y - 5z = 0
------------------
-11y + 4z = 0
z = 11y/4

Sub "z" into "x - 2y - z = 0" to find "x":
x - 2y -(11y/4) = 0
x - 19y/4 = 0
x = 19y/4

Sub "x" and "z" into "x + 9y - 5z = 0" to find "y":
(19y/4) + 9y - 5(11y/4) = 0
(19y + 36y - 55y) / 4 = 0
0y/4 = 0


So frustrated...I don't know what to do for this question. Please help me (step by step solution).

Thanks.

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