Question

If the triple scalar product $u·(v\times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Short answer

The triple scalar product $u·(v\times w)$ is equal to zero if and only if u, v and ware coplanar.

Step-by-step solution

Step 1. Given Information 

If the triple scalar product $u·(v\times w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Step 2.We have to find the relationship do the vectors u, v and w have if the triple scalar product u·(v×w) is equal to zero.

The triple scalar product is$u·(v\times w)=v·(w\times u)=w·(u\times v)$

The triple scalar product $u·(v\times w)$ is equal to zero if and only if u, v andware coplanar.