Whilst doing an exercise on the Brownian Motion on a sphere I came across this identity: $$ \langle Z\times B,Z\times B\rangle = 2|Z|^2dt $$ where $\times$ denotes the cross product and $Z$ is a diffusion process and $B$ a Brownian motion in $\mathbb{R}^3$. Does anyone have intuition for that?
Thank you!