Q. 15 - Calculus

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?

Step-by-Step Solution

Answer

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

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 and w are coplanar.