3. Cylindromania. So far, we’ve seen cylinders parallel to a coordinate axis. But there
are lots of lines that are not coordinate axes...
In this exercise, we’ll get an equation for a cylinder about a more general line through
the origin
(a) Let L be the line with vector function r(t) = ⟨t, t, t⟩. If (x, y, z) is a point in R3, use
projection to get a formula for the distance D from (x, y, z) to L.
(b) Write down the equation of the circular cylinder of radius 3 along L.
(c) Let M be the line with vector function q(t) = ⟨at, bt, ct⟩ where a, b, c in R are
constants. Describe what you would change in the calculations you did for parts (a)
and (b) in order to get the equation of the circular cylinder of radius r along M.
Do not actually find the equation for this cylinder.