## dual quaternion displacement in the Z direction by 167 and rotate 10 degrees

can someone help show me an example on how to use quaternion slerp to displace the position

64,0,0

in the Z direction by 167 and rotate 10 degrees?
Ive seen many many papers that show:

[cos(Θ/2),nsin(Θ/2)][0,0,0,0][1,0,0,0][0,tx/2,ty/2,tz/2]

and the formula to multiply these 2 dual quaternions im familiar with is:

q1q2=qr1qr2,qr1qd2+qd1qr2

therefore I have tried:

[1,0,0,0][0,64/2,0,0][cos(0.174/2),sin(0.174/2),sin(0.174/2),sin(0.174/2)][0,0,0,167/2]

which when applied to the formula to multiply looked like this:

[1,0,0,0][cos(0.174/2),sin(0.174/2),sin(0.174/2),sin(0.174/2)] , [1,0,0,0][0,0,0,167/2]+[0,64/2,0,0][cos(0.174/2),sin(0.174/2),sin(0.174/2),sin(0.174/2)]

I think im missing something as my interpretation doesnt seem to bear any fruit. if someone could point me in the right direction I would be very appreciative. thank you.