Equations for 3D Cylinders with Varying Parameters

[ydan87]

If I have a cylinder with a radius r and an axis that passes through point b with the
direction of vector n, show that its equation can be written in any of the following forms:
1) |(p-b) X n| = r
2) (p - b) X n = r.e (where e s ia unit vector orthogonal to n)
3) |(p-b) - ((p-b).n).n| = r
. = dot product
X = cross product

Thanks in advance for any guide given...

 

[HallsofIvy]

Was there a reason for titling this "3d planes equation problem" when there are no planes involved? Also, it is impossible to give any help without knowing what your symbols mean. Are we to assume that "p" is the position vector of a variable point on the cylinder?

Assuming that, what vector would $(p- b)\times n$ be?

(Also, you say that "." indicates dot product but there are two cases in which it is simply the product of a number with a vector.)

 

[ydan87]

Right, I'm sorry for the mess...
p and b are points, n is a vector and e is a unit vector as described.
Also, the | | indicates size of vector...

I'm confused with all the definitions so that's the reason for the wrong titling, sorry again...