Let \(\mathrm{ABCDEF}\) be a regular hexagon, with the vertices taken in order. The resultant of the vectors: \(\overrightarrow{AB},~\overrightarrow{BC},~\overrightarrow{CD},~\overrightarrow{DE}\) equals, in magnitude, the vector:
1. \(\overrightarrow{AB}\)
2. \(\overrightarrow{AD}\)
3. \(\sqrt2\overrightarrow{AB}\)
4. \(\sqrt3\overrightarrow{AB}\)

Subtopic:  Resultant of Vectors |
From NCERT
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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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Let \(\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},\) then:

1. \(|\overrightarrow{\mathrm{C}}|\) is always greater than \(|\overrightarrow{\mathrm{A}}|\)
2. It is possible to have \(|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|\) 
3. \(|\overrightarrow{\mathrm{C}}|\) is always equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\)
4. \(|\overrightarrow{\mathrm{C}}|\) is never equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\)
Subtopic:  Resultant of Vectors |
 59%
From NCERT
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A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are (3, \(3\)). The path of the particle makes an angle of __________ with the x-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

Subtopic:  Position & Displacement |
 76%
From NCERT
AIPMT - 2007
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The position of a moving particle at time \(t\) is \(\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:

1. \(\hat{j}-\hat{k}\) 2. \(3\hat{i}-4\hat{j}-\hat{k}\)
3. \(9\hat{i}+36\hat{j}-27\hat{k}\) 4. \(32\hat{j}-26\hat{k}\)
Subtopic:  Position & Displacement |
 81%
From NCERT
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Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

      

1.  A>B>C

2. C>A>B

3. B>A>C

4. A=B=C

Subtopic:  Position & Displacement |
 84%
From NCERT
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A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. 5 unit
2. 12 unit
3. 13 unit
4. 17 unit

Subtopic:  Position & Displacement |
 74%
From NCERT
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A particle is moving on a circular path of radius \(R.\) When the particle moves from point \(A\) to \(B\) (angle \( \theta\)), the ratio of the distance to that of the magnitude of the displacement will be:

         

1. θsinθ2

2. θ2sinθ2

3. θ2cosθ2

4. θcosθ2

Subtopic:  Position & Displacement |
 74%
From NCERT
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A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\) \((6\) m, \(7\) m) at time \(t=2\) s and \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:

1. \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) 2. \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\)
3. \(2\left ( \hat{i}+\hat{j} \right )\) 4. \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\)
Subtopic:  Speed & Velocity |
 82%
From NCERT
NEET - 2014
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The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m 
 where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:

1. \(4\) m/s \(53^\circ\) with x-axis
2. \(4\) m/s \(37^\circ\) with x-axis
3. \(5\) m/s \(53^\circ\) with y-axis
4. \(5\) m/s \(53^\circ\) with x-axis

Subtopic:  Speed & Velocity |
 66%
From NCERT
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