Vectors \(\vec {\mathrm{A}}, \vec{\mathrm{B}} \) and \(\vec{\mathrm{C}}\) are such that \(\vec{\mathrm{A}} \cdot \vec{\mathrm{B}}=0 \text { and } \vec{\mathrm{A}} \cdot \vec{\mathrm{C}}=0\). Then the vector parallel to \(\vec A\) is: 
1. \(\vec{A} \times \vec{B} \)
2. \(\vec{B}+\vec{C} \)
3. \(\vec{B} \times \vec{C} \)
4. \(\vec{B}~\text{and} ~\vec{C}\)
Subtopic:  Vector Product |
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\(\overrightarrow{A}\) and \(\overrightarrow B\) are two vectors and \(\theta\) is the angle between them. If \(\left|\overrightarrow A\times \overrightarrow B\right|= \sqrt{3}\left(\overrightarrow A\cdot \overrightarrow B\right),\) then the value of \(\theta\) will be:

1. \(60^{\circ}\) 2. \(45^{\circ}\)
3. \(30^{\circ}\) 4. \(90^{\circ}\)
Subtopic:  Scalar Product | Vector Product |
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