Problem
QUESTION 7 Quaternion Dot Product. Choose one $\cdot 5$ points Calculate the dot product $q_{1} \cdot q_{2}$ if $q_{1}=[1,-2,1,3]$ and \[ q_{2}=[1,3,2,0] \] $q_{1} \cdot q_{2}=\mathrm{u}$ $q_{1} \cdot q_{2}=-3$ $q_{1} \cdot q_{2}=3$
Solution
Step 1 ：The dot product of two quaternions is calculated by multiplying the corresponding components of the two quaternions and then adding them together.
Step 2 ：In this case, the dot product of \(q_{1}\) and \(q_{2}\) is calculated as follows: \(q_{1} \cdot q_{2} = (1*1) + (-2*3) + (1*2) + (3*0)\)
Step 3 ：So, the dot product of the two quaternions is -3.
Step 4 ：Final Answer: \(\boxed{-3}\)
