Home › MCQs › CSS Applied Mathematics › Question #4136
Back to Questions
CSS Applied Mathematics QUESTION #4136
Question 1
If $\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{b}) \times \vec{c}$, what can we conclude about vectors $\vec{a}$ and $\vec{c}$?
  • $\vec{a}$ is perpendicular to $\vec{c}$
  • $\vec{a}$ and $\vec{c}$ are parallel✔️
  • $\vec{b}$ is perpendicular to both $\vec{a}$ and $\vec{c}$
  • $\vec{a} = \vec{c}$
Correct Answer Explanation
Using vector triple product identity: $\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{a} \cdot \vec{b})\vec{c}$ and $(\vec{a} \times \vec{b}) \times \vec{c} = (\vec{a} \cdot \vec{c})\vec{b} - (\vec{b} \cdot \vec{c})\vec{a}$. Equating gives $(\vec{a} \cdot \vec{b})\vec{c} = (\vec{b} \cdot \vec{c})\vec{a}$, implying $\vec{a}$ and $\vec{c}$ are parallel.