alleryLet $\mathbf{A}=\langle 1,2,3\rangle$, $\mathbf{B}=\langle 2,0,1\rangle$, and $\mathbf{C}=\langle 0,1,1\rangle$. Then $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})$ equals
A$0$
B$1$
C$3$
D$-1$
Answer & Solution
Correct answer: D. $-1$
First find $\mathbf{B}\times\mathbf{C}=\langle 0\cdot 1-1\cdot 1,\ 1\cdot 0-2\cdot 1,\ 2\cdot 1-0\cdot 0\rangle=\langle -1,-2,2\rangle$ if computed using $\mathbf{B}=\langle 2,0,1\rangle$ and $\mathbf{C}=\langle 0,1,1\rangle$: more carefully, $\mathbf{B}\times\mathbf{C}=\langle 0\cdot 1-1\cdot 1,\ 1\cdot 0-2\cdot 1,\ 2\cdot 1-0\cdot 0\rangle=\langle -1,-2,2\rangle$.
Then $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})=1(-1)+2(-2)+3(2)=-1-4+6=1$.
**So the correct value is $1$.**
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