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Question: Answered & Verified by Expert
If $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{a} \bullet \vec{b}=0$ and
$\vec{a} \times \vec{b}=0$, then which one of the following is correct?
MathematicsVector AlgebraNDANDA 2011 (Phase 2)
Options:
  • A $\vec{a} \text { is parallel to } \vec{b}$
  • B $\vec{a}$ is perpendicular to $\vec{b}$
  • C Either $\vec{a}$ or $\vec{b}$ is a null vector
  • D None of the above
Solution:
2143 Upvotes Verified Answer
The correct answer is: Either $\vec{a}$ or $\vec{b}$ is a null vector
Let $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{a} \cdot \vec{b}=0$ and
$\vec{a} \times \vec{b}=0$ then either $\vec{a}$ or $\vec{b}$ is a null vector.

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