Let $\mathbf{A}=\langle 1,2,3\rangle$, $\mathbf{B}=\langle 2,0,1\rangl…

Question

Let $\mathbf{A}=\langle 1,2,3angle$, $\mathbf{B}=\langle 2,0,1angle$, and $\mathbf{C}=\langle 0,1,1angle$. Then $\mathbf{A}\cdot(\mathbf{B}	imes\mathbf{C})$ equals

Accepted Answer

D. $-1$

First find $\mathbf{B}	imes\mathbf{C}=\langle 0\cdot 1-1\cdot 1,\ 1\cdot 0-2\cdot 1,\ 2\cdot 1-0\cdot 0angle=\langle -1,-2,2angle$ if computed using $\mathbf{B}=\langle 2,0,1angle$ and $\mathbf{C}=\langle 0,1,1angle$: more carefully, $\mathbf{B}	imes\mathbf{C}=\langle 0\cdot 1-1\cdot 1,\ 1\cdot 0-2\cdot 1,\ 2\cdot 1-0\cdot 0angle=\langle -1,-2,2angle$. Then $\mathbf{A}\cdot(\mathbf{B}	imes\mathbf{C})=1(-1)+2(-2)+3(2)=-1-4+6=1$. So the correct value is $1$.

Answer

$0$

Answer

$1$

Answer

$3$

Let $\mathbf{A}=\langle 1,2,3\rangle$, $\mathbf{B}=\langle 2,0,1\rangle$, and $\mathbf{C}=\langle 0,1,1\rangle$. Then $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})$ equals