Question

If u, v, and ware three mutually orthogonal vectors in ${\mathrm{ℝ}}^3$, explain why $u\times (v\times w)=0$.

Short answer

$u\times (v\times w)=0$because$u\times (v\times w)=(u·w)v-(u·v)w$andu, v, and ware three mutually orthogonal vectors.

Step-by-step solution

Step 1. Given Information  

If u, v, and ware three mutually orthogonal vectors in ${\mathrm{ℝ}}^3$, explain why $u\times (v\times w)=0$.

Step 2. It is given that u, v, and w are three mutually orthogonal vectors in ℝ3.

As we know that $u\times (v\times w)=(u·w)v-(u·v)w$

Since u, v, and ware three mutually orthogonal so the $u·w\mathrm{and}u·v$is zero.

So

$$\begin{gathered} u\times (v\times w)=0\times v-0\times w \\ u\times (v\times w)=0 \end{gathered}$$