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:  Resolution of Vectors |
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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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Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are

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 the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

1. 90°

2. 45°

3. 180°

4. 0°

Subtopic:  Resultant of Vectors |
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Six vectors  have the directions indicated in the figure. Which of the following statements may be true?

(a) $\stackrel{\to }{b}+\stackrel{\to }{c}=\stackrel{\to }{-f}$                        (b) $\stackrel{\to }{d}+\stackrel{\to }{c}=\stackrel{\to }{f}$

(c) $\stackrel{\to }{d}+\stackrel{\to }{e}=\stackrel{\to }{f}$                        (d) $\stackrel{\to }{b}+\stackrel{\to }{e}=\stackrel{\to }{f}$

Subtopic:  Resultant of Vectors |
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In the given figure

(A)  Angle between $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ is $110°$

(B)  Angle between $\stackrel{\to }{\mathrm{C}}$ and $\stackrel{\to }{\mathrm{D}}$ is $60°$

(C)  Angle between $\stackrel{\to }{\mathrm{B}}$ and $\stackrel{\to }{\mathrm{C}}$ is $110°$

(D)  Angle between $\stackrel{\to }{\mathrm{B}}$ and $\stackrel{\to }{\mathrm{C}}$ is $70°$

Subtopic:  Resultant of Vectors |
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A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

(A)  1 N

(B)  11 N

(C)  15 N

(D)  20 N

Subtopic:  Resultant of Vectors |
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Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

(A)  2, 4, 8

(B)  4, 8, 16

(C)  1, 2, 1

(D)  0.5, 1, 2

Subtopic:  Resultant of Vectors |
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