The position of a particle in a rectangular co-ordinate system is (3, 2, 5). Then its position vector will be:

1. $5\stackrel{^}{\mathrm{i}}+6\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$

2. $3\stackrel{^}{\mathrm{i}}+2\stackrel{^}{\mathrm{j}}+5\stackrel{^}{\mathrm{k}}$

3. $5\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$

4. None of these

Subtopic:  Scalars & Vectors |
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A scalar quantity is one that:

1. is conserved in a process.

2. will never accept negative values.

3. must be dimensionless.

4. has the same value for observers with different orientations of axes.

Subtopic:  Scalars & Vectors |
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If $\stackrel{\to }{\mathrm{a}}$ is a vector and x is a non-zero scalar, then which of the following is correct?
1. xa is a vector in the direction of $\stackrel{\to }{\mathrm{a}}$
2.  xa is a vector collinear to $\stackrel{\to }{\mathrm{a}}$
3.  xa and $\stackrel{\to }{\mathrm{a}}$ have independent directions
4.  xa is a vector perpendicular to $\stackrel{\to }{\mathrm{a}}$

Subtopic:  Scalars & Vectors |
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A force of 20 N acts on a particle along a direction, making an angle of 60° with the vertical. The component of the force along the vertical direction will be

1. 2 N

2. 5 N

3. 10 N

4. 20 N

Subtopic:  Resolution of Vectors |
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If $\stackrel{\to }{\mathrm{A}}=2\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}-5\stackrel{^}{\mathrm{k}}$, then the direction cosines of the vector are:

(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three +ve coordinate axes.)

1.

2.

3.

4.

Subtopic:  Resolution of Vectors |
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$\stackrel{\to }{\mathrm{A}}$ is a vector with magnitude A, then the unit vector $\stackrel{^}{\mathrm{A}}$ in the direction of $\stackrel{\to }{\mathrm{A}}$ is

1. $\mathrm{A}\stackrel{\to }{\mathrm{A}}$

2. $\stackrel{\to }{\mathrm{A}}.\stackrel{\to }{\mathrm{A}}$

3. $\stackrel{\to }{\mathrm{A}}×\stackrel{\to }{\mathrm{A}}$

4. $\stackrel{\to }{\mathrm{A}}/\mathrm{A}$

Subtopic:  Resolution of Vectors |
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A force F applied at a 30° angle to the x-axis has the following X and Y components:

1.

2.

3.

4.

Subtopic:  Resolution of Vectors |
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A child pulls a box with a force of  at an angle of $60°$above the horizontal. Then the horizontal and vertical components of the force will be:

1. 100 N, 175 N

2.  86.6 N, 100 N

3.  100 N, 86.6 N

4. 100 N, 0 N

Subtopic:  Resolution of Vectors |
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If  $\stackrel{\to }{A}=3\stackrel{^}{i}+4\stackrel{^}{j}$ and $\stackrel{\to }{B}=7\stackrel{^}{i}+24\stackrel{^}{k}$, then the vector having the same magnitude as that of $\stackrel{\to }{B}$ and parallel to $\stackrel{\to }{A}$ is:

1.

2. $\frac{7}{5}\stackrel{^}{i}+\frac{24}{5}\stackrel{^}{j}$

3. $20\stackrel{^}{i}+15\stackrel{^}{j}$

4.

Subtopic:  Resolution of Vectors |
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A force is 60 ° inclined to the horizontal. If its rectangular component in the horizontal direction is 50 N, then the magnitude of the force in the vertical direction is

1. 25 N

2. 75 N

3. 87 N

4. 100 N

Subtopic:  Resolution of Vectors |
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