Answer:
The value of [tex]a\cdot b\times c[/tex] is 0.
Explanation:
The three vectors provided are:
[tex]a=2i-3j+7k\\b= i+2k\\c=j-k[/tex]
The value to be computed is:
[tex]a\cdot b\times c[/tex]
Compute the value of (b × c) as follows:
[tex]b\times c=\left|\begin{array}{ccc}i&j&k\\1&0&2\\0&1&-1\end{array}\right|[/tex]
[tex]=\left|\begin{array}{cc}0&2\\1&-1\end{array}\right|i-\left|\begin{array}{cc}1&2\\0&-1\end{array}\right|j+\left|\begin{array}{cc}1&0\\0&1\end{array}\right|k\\\\=-2i+1j+1k[/tex]
Now compute the value of [tex]a\cdot b\times c[/tex] as follows:
[tex]a\cdot b\times c=(2i-3j+7k)\cdot (-2i+j+k)[/tex]
[tex]=(2\cdot -2)+(-3\cdot 1)+(7\cdot1)\\\\=-4-3+7\\\\=0[/tex]
Thus, the value of [tex]a\cdot b\times c[/tex] is 0.
