ECON 330 Midterm: ECON 330 UW Madison answerkey2 MidtermSpring2001
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Solution: a normal vector ~v is the cross product of the vector h3, 2, 4i from one given point to the other and h1, 1, 1i. Since h1, 0, 2i is in the plane, an equation for the plane is 6(x 1) + (y 0) + 5(z + 2) = 0, or simplifying: 6x + y + 5z = 16: (15 points) find an equation for the surface in (x, y, z)-space obtained by rotating the ellipse x2 + 4y2 = 1 of the (x, y)-plane about the x-axis. Solution: the distance from the x-axis is py2 + z2, which replaces |y| in the given equa- tion. Find an equation for the plane which contains both lines. Solution: a vector in the direction of the rst line is ~u = 2~i ~j 2~k, and for the second line ~w = ~i + 2~j + 2~k. So a normal vector ~v to the plane is the cross product:
