# Quaternion-Vector transformation

I have the following problem:

Rotations can be done by using quaternions. My understanding is, that to rotate a vector around a quaternion, the vector has to be transformed to a 4-dimensional vector: v = [x,y,z] to v'= [0,x,y,z] This vector can now be rotated around the quaternion using v'2 = q*v'*q' where q' is the conjugate quaternion and the quaternion product needs to be used.

My problem is, I don't understand how to get a 3D vector from the new, 4-dimensional vector v'2 since v'2 = [w,ai,bj,ck]. Do I just disregard w and use v_new = [a,b,c] as my new vector or do I have to do a specific transformation?

• Unless you did something wrong you should automatically have $w=0$ after computing $qv'q'$. But, yes, $v_{new}=(a,b,c)$, where $qv'q'=ai+bj+ck$ – Jyrki Lahtonen Sep 7 '18 at 6:02
• That's it! Thank you very much!! – Robert Reichel Sep 7 '18 at 8:48
• Glad to help! By the way, a namesake of yours is an international level hockey star (originally from the Czech republic). Are you related by any chance :-) – Jyrki Lahtonen Sep 7 '18 at 10:32
• No, unfortunately not. I found out about that when I googled myself but sadly I don't know him :( – Robert Reichel Sep 7 '18 at 11:54