Question

In Problem, use the given vectors u, v, and w to find the given expression.

$$\begin{gathered} \left(w\times w\right)\times v \\ u=2i-3j+k \\ v=-3i+3j+2k \\ w=i+j+3k \end{gathered}$$

Short answer

The resultant of the given equation is : 0

Step-by-step solution

Step1. Given information

$$\begin{gathered} vectors \\ u=2i-3j+k \\ v=-3i+3j+2k \\ w=i+j+3k \end{gathered}$$

equation:$\left(W\times W\right)\times V$

Step2. calculating the equation 

We know that

$$\begin{gathered} x=ai+bj+ck \\ y=pi+qj+rk \\ x\times y=\left|\begin{array}{ccc}i& j& k\\ a& b& c\\ p& q& r\end{array}\right| \end{gathered}$$

so according to question

$$\begin{gathered} \left(w\times w\right)=\left|\begin{array}{ccc}i& j& k\\ 1& 1& 3\\ 1& 1& 3\end{array}\right|=\left[i\left|\begin{array}{cc}1& 3\\ 1& 3\end{array}\right|-j\left|\begin{array}{cc}1& 3\\ 1& 3\end{array}\right|+k\left|\begin{array}{cc}1& 1\\ 1& 1\end{array}\right|\right] \\ \left(w\times w\right)=0 \\ \left(w\times w\right)\times v=0\times v=0 \end{gathered}$$