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

in the Z direction by 167 and rotate 10 degrees?

Ive seen many many papers that show:

[*c**o**s*(Θ/2),*n**s**i**n*(Θ/2)][0,0,0,0]∗[1,0,0,0][0,*t**x*/2,*t**y*/2,*t**z*/2]

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

*q*1*q*2=*q**r*1*q**r*2,*q**r*1*q**d*2+*q**d*1*q**r*2

therefore I have tried:

[1,0,0,0][0,64/2,0,0]∗[*c**o**s*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(0.174/2)][0,0,0,167/2]

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

[1,0,0,0]∗[*c**o**s*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(0.174/2)] , [1,0,0,0]∗[0,0,0,167/2]+[0,64/2,0,0]∗[*c**o**s*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(0.174/2),*s**i**n*(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.

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