Lomion
Oct19-04, 10:21 PM
This is a question from a past midterm that I'd appreciate some help with. It deals with the gradient as a normal. I'm not having trouble actually obtaining the gradient, but I am having trouble with some of the geometry involved, so any help would be appreciated!
Consider the function:
y = \sqrt{x^2 + z^2}
Give the equation for 2 planes whose intersection is the normal line to this surface at (1,4,\sqrt{15}).
I found the value: \nabla f(1,4,\sqrt{15}) = (1/4, -1, \sqrt{15}/4).
And the equation for the normal line is:
r(t) = (1,4,\sqrt{15}) + t(1/4, -1, \sqrt{15}/4)
My question is: How do I find two planes that intersect in this line?
I think I should parametrize the variables, so
x = 1 + 1/4t
y = 4 - t
z = \sqrt{15} + \sqrt{15}/4 * t
But that's where I get lost. Can someone just point me in the right direction in terms of what equations to set up?
Thanks!
Consider the function:
y = \sqrt{x^2 + z^2}
Give the equation for 2 planes whose intersection is the normal line to this surface at (1,4,\sqrt{15}).
I found the value: \nabla f(1,4,\sqrt{15}) = (1/4, -1, \sqrt{15}/4).
And the equation for the normal line is:
r(t) = (1,4,\sqrt{15}) + t(1/4, -1, \sqrt{15}/4)
My question is: How do I find two planes that intersect in this line?
I think I should parametrize the variables, so
x = 1 + 1/4t
y = 4 - t
z = \sqrt{15} + \sqrt{15}/4 * t
But that's where I get lost. Can someone just point me in the right direction in terms of what equations to set up?
Thanks!