Topic: Electromagnetics
If A, B and C are vectors and $A=1\cdot u_{x}+2\cdot u_{y}+3\cdot u_{z},$ $B=1\cdot u_{x}+1\cdot u_{y}+1\cdot u_{z}$ and $C=3\cdot u_{x}+2\cdot u_{y}+1\cdot u_{z}$ then $(A\times B)\cdot C$ is
- A. 2
- B. 1
- C. 0
- D. -1
Answer: C. 0
Explanation: $\vec{A}=1\hat{u}_{x}+2\hat{u}_{y}+3\hat{u}_{z}$, $\vec{B}=1\hat{u}_{x}+1\hat{u}_{y}+1\hat{u}_{z}$, $\vec{C}=3\hat{u}_{x}+2\hat{u}_{y}+1\hat{u}_{z}$. $(\vec{A}\times\vec{B}) = -\hat{u}_{x}+2\hat{u}_{y}-\hat{u}_{z}$. $(\vec{A}\times\vec{B})\cdot\vec{C} = (-\hat{u}_{x}+2\hat{u}_{y}-\hat{u}_{z})\cdot(3\hat{u}_{x}+2\hat{u}_{y}+1\hat{u}_{z}) = 0$.