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!!