# How do I multiply quaternion and vector?

I started with this

```
N.<c,d,a1,a2,a3,a4,b1,b2,b3,b4,s> = QQ[]
H.<i,j,k> = QuaternionAlgebra(c,d)
a = a1 + a2 * i + a3 * j + a4 * k
b = b1 + b2 * i + b3 * j + b4 * k
a+b
a*b
```

but the next step does not work

```
gravity = vector([0, 0, 1])
a * gravity * a.conjugate()
```