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CSS Applied Mathematics QUESTION #4140
Question 1
If $\vec{a} \cdot (\vec{b} \times \vec{c}) = 0$, what does this imply?
  • $\vec{a}$ is perpendicular to $\vec{b}$
  • $\vec{a}$, $\vec{b}$, $\vec{c}$ are coplanar✔️
  • $\vec{b}$ is parallel to $\vec{c}$
  • $\vec{a} = \vec{0}$
Correct Answer Explanation
The scalar triple product $\vec{a} \cdot (\vec{b} \times \vec{c})$ equals the volume of the parallelepiped formed by the three vectors. If zero, the vectors are coplanar (linearly dependent).