Fanny point x E S2 \ N, let t be the unique straight line through (0,0, I) and x. Since x 7t N, t intersects the
(xi, x2)-plane P {r3 = 0). Then f(x) E R2 is defined to be the point whose coordinates (xi, x2) which agree
with the (xl, x2) coordinates of the intersection point of t with the plane P. (I) Consider the point x = (4,0, 4).
Show that x is a point in S2. Calculate the linear parametric equation (x(t) = At + B, y(t) = Ct + D, z(t) = Et +
F) for the line t that passes through x and N. Calculate where l intersects the plane P, and write down 1(x).
(2) For a general point x = (x9, yo, zo) E 52 N, calculate the linear parametric equation for the line t that
passes through x and N (in terms of the constants xo, yo, and zo). Then calculate where t intersects the
plane P, to determine ,f(x) in terms of ro, yo, zo. This gives a general formula for the function 1. (3)
Looking at your function from problem 2, what is the set of points (x0, yo, zo) ERs where this function is
defined? Show this function is continuous where it is defined.