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Consider two planes kx + y + z − k = 0 and kz − ky + x = −1 for a real number k. (a) Find the line of intersection of the planes L. (b) As the value of k varies, the line L will trace out some surface S. Find a parametric equation for the curve of intersection of the surface S and the plane z = c. (c) Find the volume bounded by S and the planes z = 0 and z = 1.

Consider two planes kx + y + z − k = 0 and kz − ky + x = −1 for a real number k.
(a) Find the line of intersection of the planes L.
(b) As the value of k varies, the line L will trace out some surface S. Find a parametric equation for
the curve of intersection of the surface S and the plane z = c.
(c) Find the volume bounded by S and the planes z = 0 and z = 1.

Grade:12th Pass

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