Let P be the plane z = 1. Let m be a line of the form (a, b, c) + t(1,0, -1), t

Question

Let P be the plane z = 1. Let m be a line of the form (a, b, c) + t(1,0, -1), t element of R, where (a,b,c) element of R^3. Prove the following by direct computation with the given lines and planes. Show that m contains the origin if and only if a = - c and 6 = 0. Assume that m contains the origin. Find its image under central projection to P. For the remainder of the question, assume that m does not contain the origin. Find the point on m that does not have an image under central projection to P. Find the image of m under central projection to P. By reparametrizing your result, show that the image is a line in P that passes through, but omits, the point (-1, 0, 1).

Explanation / Answer

a)

(a,b,c)+t(1,0,-1)=(0,0,0)

then

a+t=0 ,b=0 ,c-t=0

then, a=-c and b=0

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