Chapter 11, Problem 76RE

To determine

Determine whether the statement is true or false.

Answer to Problem 76RE

The given statement is true.

Explanation of Solution

Given:

The triple scalar product of three vectors in space is a scalar.

Consider the following vectors u,v and w.

  $u=\langle 3,4,4\rangle ,v=\langle 2,3,0\rangle andw=\langle 0,0,6\rangle$

The triple scalar product of three non-zero vectors is $u\left(v\times w\right)$ and hence,

  $\begin{array}{l}u•\left(v\times w\right)=\left|\begin{array}{ccc}3& 4& 4\\ 2& 3& 0\\ 0& 0& 6\end{array}\right|\hfill \\ =3\left[3\left(6\right)–0\left(0\right)\right]–4\left[2\left(6\right)–0\left(0\right)\right]+4\left[2\left(0\right)–3\left(0\right)\right]\hfill \\ =54–48\hfill \\ =6\hfill \end{array}$

Therefore, it is true that the triple scalar product of three vectors in space is a scalar.

Hence, the given statement is true.