Given: Three points $A,B$ and $C$ and the force vector $F.$ Force $F$ is applied at point $A.$

Point $A$ is located at $5$hat$()-11$hat$()+7$hat$(k)$ meters.

Point $B$ is located at $4$hat$()+12$hat$()-5$hat$(k)$ meters.

Point $C$ is located at $-2$hat$()+7$hat$()+2$hat$(k)$ meters.

Force $F$ is given by $150$hat$()+2$hat$()-75$hat$(k)$ Newtons.

Find: the moment about a line from point $B$ to point $C$ from force $F.$ Express as a vector. $(30$

points$)$