# Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is  (1) ${\mathrm{cos}}^{-1}\left(-\frac{17}{18}\right)$ (2) ${\mathrm{cos}}^{-1}\left(-\frac{1}{3}\right)$ (3) ${\mathrm{cos}}^{-1}\left(\frac{2}{3}\right)$ (4) ${\mathrm{cos}}^{-1}\left(\frac{8}{9}\right)$

Subtopic:  Resultant of Vectors |
68%
From NCERT
PMT - 1999
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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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If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is

(1) $5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /3$

(2) $5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /4$

(3) $-5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /3$

(4) $-5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /4$

Subtopic:  Resultant of Vectors |
85%
From NCERT
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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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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:

$1.$ ${0}^{0}$
$2.$ ${90}^{0}$
$3.$ ${45}^{0}$
$4.$ ${180}^{0}$

Subtopic:  Resultant of Vectors |
74%
AIPMT - 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 |
81%
From NCERT
NEET - 2016
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If vectors A = cosωt $\stackrel{^}{i}$ + sinωt $\stackrel{^}{j}$ and B = (cosωt/2) $\stackrel{^}{i}$ + (sinωt/2) $\stackrel{^}{j}$ are functions of time, then the value of t at which they are orthogonal to each other

1. t=$\mathrm{\pi }$/4ω
2. t=$\mathrm{\pi }$/2ω
3. t=$\mathrm{\pi }$
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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 Assertion (A): The graph between P and Q is a straight line when 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.

Which one, of the following statements, is correct?

 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 |
77%
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Two forces A and B have a resultant ${R}_{1}$. If B is doubled, the new resultant ${R}_{2}$ is perpendicular to A. Then

1. ${R}_{1}=A$

2. ${R}_{1}=B$

3. ${R}_{2}=A$

4. ${R}_{2}=B$

Subtopic:  Resultant of Vectors |
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