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Question 1116903: How to write the equation of the line, when the 3 planes (with equations below) intersect in a line if k=-2?
x+y+z=0
kx+y-2z=-6
2y+(k+2)z=k-2
I found the value of k=-2, but not sure how to write the equation of the line.
1) rectangular form 2) vector form.
Thank you.
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
At k= -2 your system has the form
x + y + z = 0
-2x + y - 2z = -6
2y = -4.
Last equation gives y = -2 and, after substituting this value of y into two other equations, gives you the system
x + z = 2
-2x - 2z = -4
It is equivalent to the system
x + z = 2
x + z = 2,
Which is, actually, ONE equation
x + z = 2.
Thus the equations in 3D space of the straight line under the question are these two equations
y = -2,
x + z = 2.
It is the answer in rectangular form.
In vector form the parametric equation for this straight line is
V(t) = (t,-2,2-t), where t is the parameter (= any real number).
Solved.
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