# Two forces A and B have a resultant ${R}_{1}$. If B is doubled, the new resultant ${R}_{2}$ is perpendicular to A. Then1. ${R}_{1}=A$2. ${R}_{1}=B$3. ${R}_{2}=A$4. ${R}_{2}=B$

Subtopic:  Resultant of Vectors |
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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 |
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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 |
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PMT - 1990
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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 |
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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%
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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 |
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If the angle between the vector  is  $\theta$, the value of the product $\left(\stackrel{\to }{B}×\stackrel{\to }{A}\right).\stackrel{\to }{A}$ is equal to:

1.

2.

3.

4. zero

Subtopic:  Vector Product |
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Given that $$\overrightarrow {C}= \overrightarrow {A}+\overrightarrow {B}$$$\mathrm{and}$$$\overrightarrow {C}$$ makes an angle $\mathrm{}$$$\alpha$$ with $$\overrightarrow {A}$$ and $$\beta$$ with $$\overrightarrow {B}$$. Which of the following options is correct?
1. $$\alpha$$ cannot be less than $$\beta$$
2. $$\alpha <\beta, ~\text{if}~A<B$$
3. $$\alpha <\beta, ~\text{if}~A>B$$
4. $$\alpha <\beta, ~\text{if}~A=B$$

Subtopic:  Resultant of Vectors |
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Component of $3\stackrel{^}{i}+4\stackrel{^}{j}$ perpendicular to $\stackrel{^}{i}+\stackrel{^}{j}$ and in the same plane as that of $3\stackrel{^}{i}+4\stackrel{^}{j}$ is:

1. $\frac{1}{2}\left(\stackrel{^}{j}-\stackrel{^}{i}\right)$

2. $\frac{3}{2}\left(\stackrel{^}{j}-\stackrel{^}{i}\right)$

3. $\frac{5}{2}\left(\stackrel{^}{j}-\stackrel{^}{i}\right)$

4. $\frac{7}{2}\left(\stackrel{^}{j}-\stackrel{^}{i}\right)$

Subtopic:  Scalar Product |
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Two forces, $$1$$ N and $$2$$ N, act along with the lines $$x=0$$ and $$y=0$$. The equation of the line along which the resultant lies is given by:
1. $$y-2x =0$$
2. $$2y-x =0$$
3. $$y+x =0$$
4. $$y-x =0$$

Subtopic:  Resultant of Vectors |
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