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Let's say we have 2 quaternions a = 1+3i+5j+7k, b = 3+8i+12j+16k, can I multiply its norm to another quaternion? For example: ||a||(b)

Norm of a = $\sqrt{1^2+3^2+5^2+7^2}$ = 9.16515...

Should I do it like simple maths? 9.16515(3+8i+12j+16k) = 27.49 + 73.32i + 109.98j + 146.64

Or should I turn the norm into a quaternion first(9.16515+9.16515i+9.16515j+9.16515k), then calculate the Hamilton product of them? Multiplication Method

Thank you for your help!!

ki.c
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  • What are you trying to do? Do you just want to scale a quaternion by the length/norm of another one or do you want to multiply them together and then determine the norm of the product? – Tyberius Oct 13 '21 at 15:03
  • I need to calculate something like this, so I guess multiplying? Equation – ki.c Oct 13 '21 at 15:20
  • If the equation has you multiplying by just the norm, then do that. You can do the simple version you described. Turning the norm into a different quaternion will not make sense. – Tyberius Oct 13 '21 at 15:36

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