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CSS Applied Mathematics QUESTION #1320
Question 1
If two vectors \(\vec{a}\) and \(\vec{b}\) satisfy \(\vec{a}\times\vec{b}=\vec{0}\) and \(\vec{a}\neq\vec{0}\), \(\vec{b}\neq\vec{0}\), then:
  • They are perpendicular
  • They are parallel✔️
  • Their magnitudes are equal
  • Their dot product is zero
Correct Answer Explanation
The cross product \(\vec{a}\times\vec{b}=|\vec{a}||\vec{b}|\sin\theta\,\hat{n}\). If \(\vec{a}\times\vec{b}=\vec{0}\) and neither vector is zero, then \(\sin\theta=0\Rightarrow\theta=0\) or \(\pi\), meaning the vectors are parallel (or anti-parallel).