If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)

Subtopic:  Scalar Product |
 59%
From NCERT
NEET - 2015
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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 |
 68%
From NCERT
NEET - 2013
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Six vectors a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? 

1. b+c=f

2. d+c=f

3. d+e=f

4. b+e=f

Subtopic:  Resultant of Vectors |
 74%
From NCERT
AIPMT - 2010
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Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is:
                 

1.  0.5 N

2.  1.5 N

3.  34 N

4.  3 N

Subtopic:  Resultant of Vectors |
 52%
From NCERT
AIPMT - 2008
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A and B are two vectors and θ is the angle between them. If A×B=3A.B, then the value of θ will be:

1. 60o 2. 45o
3. 30o 4. 90o
Subtopic:  Scalar Product | Vector Product |
 80%
From NCERT
AIPMT - 2007
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The vectors A and B are such that: A+B=A-B.
The angle between the two vectors is:
1. \(90^\circ\)
2. \(60^\circ\)
3. \(75^\circ\)
4. \(45^\circ\)

Subtopic:  Resultant of Vectors |
 80%
From NCERT
AIPMT - 2006
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