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Question: Answered & Verified by Expert
Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of points $A, B, C$ respectively. Under which one of the following conditions are the points $A, B, C$ collinear?
MathematicsVector AlgebraNDANDA 2009 (Phase 1)
Options:
  • A $\quad \vec{a} \times \vec{b}=\overrightarrow{0}$
  • B $\vec{b} \times \vec{c}$ is parallel to $\vec{a} \times \vec{b}$
  • C $\vec{a} \times \vec{b}$ is perpendicular to $\vec{b} \times \vec{c}$
  • D $(\vec{a} \times \vec{b})+(\vec{b} \times \vec{c})+(\vec{c} \times \vec{a})=\overrightarrow{0}$
Solution:
2160 Upvotes Verified Answer
The correct answer is: $(\vec{a} \times \vec{b})+(\vec{b} \times \vec{c})+(\vec{c} \times \vec{a})=\overrightarrow{0}$
Points A, B and $\mathrm{C}$ are collinear, if
$(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})+(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})+(\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}})=\overrightarrow{0}$

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