A difficult (for me) 3d shapes problem

[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
. = vector-vector dot product
X = vector-vector cross product

Thanks in advance for any guide given...

 

[tiny-tim]

hi ydan87!

start by translating each of 1) 2) and 3) into ordinary english …

what do you get? ​

 

[ydan87]

Tiny tim
1) the length of the vector you get by the cross product of the vector from point p to point b and normal n equals to r, the radius of the cylinder.
2) the vector you get by the cross product above equals to the vector you get by multiplying scalar r with vector e, which is a unit vector orthogonal to n.
If you guide me through those i'll be ok with 3.

Is it clearer now?

 

[tiny-tim]

1) the length of the vector you get by the cross product of the vector from point p to point b and normal n equals to r, the radius of the cylinder.
2) the vector you get by the cross product above equals to the vector you get by multiplying scalar r with vector e, which is a unit vector orthogonal to n.

ok

now also use the words "cos" or "sin" ​

 

[ydan87]

Can you please explain what you mean? I can't give you the parametric representation if that's what you mean...

 

[tiny-tim]

i meant explain what the cross product is, instead of just saying "cross product"!