If \(\vec F=2\hat i+\hat j-\hat k\) and \(\vec r=3\hat i+2\hat j-2\hat k,\) then the scalar and vector products of \(\vec F\) and \(\vec r\) have the magnitudes, respectively, as:
1.  \(5, ~\sqrt3\)
2.  \(4,~ \sqrt5\)
3.  \(10, ~\sqrt2\)
4.  \(10,~2\)
Subtopic:  Vector Product |
 75%
From NCERT
NEET - 2022
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A particle moves from a point \(\left(\right. - 2 \hat{i} + 5 \hat{j} \left.\right)\) to \(\left(\right. 4 \hat{j} + 3 \hat{k} \left.\right)\) when a force of \(\left(\right. 4 \hat{i} + 3 \hat{j} \left.\right)\) \(\text{N}\) is applied. How much work has been done by the force?

1. \(8\) J 2. \(11\) J
3. \(5\) J 4. \(2\) J
Subtopic:  Scalar Product |
 63%
From NCERT
NEET - 2016
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If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?
1. \(90^\circ\)
2. \(45^\circ\)
3. \(180^\circ\)
4. \(0^\circ\)
Subtopic:  Resultant of Vectors |
 82%
From NCERT
NEET - 2016
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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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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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If a vector (2i^+3j^+8k^) is perpendicular to the vector (4i^-4j^+αk^), then the value of α is:

1. -1

2. -12

3. 12

4. 1

Subtopic:  Scalar Product |
 75%
From NCERT
AIPMT - 2005
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If the angle between the vector A and B is θ, the value of the product (B×A)A is equal to:

1. zero

2. BA2sinθcosθ

3. BA2cosθ

4. BA2sinθ

Subtopic:  Scalar Product | Vector Product |
 59%
From NCERT
AIPMT - 2005
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