Answer:
0
Step-by-step explanation:
three vectors are
[tex]u=(2,3,4)-(1,2,1)=(1,1,3)[/tex]
[tex]v=(3,4,5)-(1,2,1)=(2,2,4)[/tex]
[tex]w=(2,3,2)-(1,2,1)=(1,1,1)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 2 & 2 & 4 \\ 1 & 1 & 1\end{array}\right|=(-2,2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
2
three vectors are [tex]u=(4,4,6)-(3,3,3)=(1,1,3)[/tex]
[tex]v=(4,4,4)-(3,3,3)=(1,1,1)[/tex]
[tex]w=(5,5,7)-(3,3,3)=(2,2,4)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 1 & 1 & 1 \\ 2 & 2 & 4\end{array}\right|=(2,-2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
