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 |
 81%
From NCERT
NEET - 2016
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If vectors A = cosωt i^ + sinωt j^ and B = (cosωt/2) i^ + (sinωt/2) j^ are functions of time, then the value of t at which they are orthogonal to each other

1. t=π/4ω
2. t=π/2ω
3. t=π
4. t=0 

 

Subtopic:  Scalar Product |
 54%
From NCERT
NEET - 2015
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Six vectors \(\overrightarrow a ~\text{through}~\overrightarrow f\) have the directions as indicated in the figure. Which of the following statements may be true?

      
1. \(\overrightarrow b + \overrightarrow c = -\overrightarrow f\)
2. \(\overrightarrow d + \overrightarrow c = \overrightarrow f\)
3. \(\overrightarrow d + \overrightarrow e = \overrightarrow f\)
4. \(\overrightarrow b + \overrightarrow e = \overrightarrow f\)

Subtopic:  Resultant of Vectors |
 65%
From NCERT
NEET - 2010
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If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

 1. 00
2. 900
3. 450
4. 1800

Subtopic:  Resultant of Vectors |
 74%
AIPMT - 2016
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If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is 

(1) 52,  π/3

(2) 52,  π/4

(3) 52,  π/3

(4) 52,  π/4

Subtopic:  Resultant of Vectors |
 85%
From NCERT
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Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)

Subtopic:  Resultant of Vectors |
 64%
From NCERT
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Two forces with equal magnitudes \(F\) act on a body and the magnitude of the resultant force is \(\frac{F}{3}\). The angle between the two forces is: 
1. \(\cos^{- 1} \left(- \frac{17}{18}\right)\)
2. \(\cos^{- 1} \left(- \frac{1}{3}\right)\)
3. \(\cos^{- 1} \left(\frac{2}{3}\right)\)
4. \(\cos^{- 1} \left(\frac{8}{9}\right)\)

Subtopic:  Resultant of Vectors |
 68%
From NCERT
PMT - 1999
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Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is 

(1) 45°

(2) 120°

(3) 150°

(4) 60°

Subtopic:  Resultant of Vectors |
 74%
From NCERT
PMT - 1990
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Given below are two statements:
Assertion (A): The graph between \(P\) and \(Q\) is a straight line when \(\frac{P}{Q}\) is constant.
Reason (R): The straight-line graph means that \(P\) is proportional to \(Q\) or \(P\) is equal to a constant multiplied by \(Q\).
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False 
Subtopic:  Co-ordinate geometry |
 78%
From NCERT
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Two forces A and B have a resultant R1. If B is doubled, the new resultant R2 is perpendicular to A. Then

1. R1=A

2. R1=B

3. R2=A

4. R2=B

Subtopic:  Resultant of Vectors |
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