Find the parametric equations of the line of intersection of the
planes x − z = 1 and y + 2z = 3. (b) Find an equation of the plane
that contains the line of intersection above and it is
perpendicular to the plane x + y − 2z = 1.
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.)
z = x2 +
y2, z = 16 −
y, (4, −1, 17)
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.) z = sqrt(x2 +
y2) , 9x − 3y + 5z = 40, (3, 4, 5)
Question: (a) Find parametric equations for the line of
intersection of the planes given by 3x − 2y + z = 1 and 2x + y − 3z
= 3.
(b) Find the equation of the plane orthogonal to both of these
planes and passing through the point (−2, 1, 1).
Let C be a plane curve parameterized by arc length by α(s), T(s)
its unit tangent vector and N(s) be its unit normal vector. Show d
dsN(s) = −κ(s)T(s).