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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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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Given that  makes an angle . Which of the following options is correct?

1.

2.

3.

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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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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Assertion: The graph between P and Q is a straight line when P/Q is constant.
Reason: 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. If both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
2. If both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
3. If the assertion is true but the reason is false.
4. If the assertion and reason are both 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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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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Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 N

Subtopic:  Resultant of Vectors |
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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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