SUPER CONFUSING linear algebra question

[theBEAST]

SUPER CONFUSING linear algebra question :)

Homework Statement

I have attached a picture of the question with a solution.

The Attempt at a Solution

Well... First i found the parametric equation of the vector L... Yeah...

So even looking at the solution I am confused. I get the conversion that they made to rad/s but the steps after that blow my mind :|. What does omega mean and also why did they multiply by (1,1,1) and then took the cross product of this point and the direction of the rod?

I want to get through this step by step.

Thank you!

 

[susskind_leon]

where's the pic ;)

 

[theBEAST]

where's the pic ;)

Wow I was so excited I forgot about the picture LOOL

 

[susskind_leon]

Lol
So, Omega means angular velocity (how many rads per unit time, in this case, minute). You should look it up on wikipedia, it reveals useful information for you.
Omega vector is the angular velocity times the unit vector of the rotation axis, which is (1,1,1)/sqrt(3)
Now, rotation axis cross position vector equals velocity is a general relation.
(If you don't believe me, look at a circularly rotating particle in the xy-plane, for example. Compute the velocity by taking d/dt r(vec). You will see, it holds. Now do the same in the xz- and yz-plane and argue that you can choose any plane.)
Now you only need to take the length of v and you're done.