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

1. 5i^+6j^+2k^

2. 3i^+2j^+5k^

3. 5i^+3j^+2k^

4. None of these

Subtopic:  Scalars & Vectors |
 93%
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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 |
 61%
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If \(\vec{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
1. \(x\vec{a}\) is a vector in the direction of \(\vec{a}\)
2. \(x\vec{a}\) is a vector collinear to \(\vec{a}\)
3. \(x\vec{a}\) and \(\vec{a}\) have independent directions
4. \(x\vec{a}\) is a vector perpendicular to \(\vec{a}\)

Subtopic:  Scalars & Vectors |
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A force of \(20\) N acts on a particle along a direction, making an angle of \(60^\circ\) 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 |
 89%
From NCERT
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If A=2i^+4j^-5k^, 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. 245, 445 and -545

2. 145, 245 and 345

3. 445, 0 and 445

4. 345, 245 and 545

Subtopic:  Resolution of Vectors |
 88%
From NCERT
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A is a vector with magnitude A, then the unit vector A^ in the direction of A is

1. AA

2. A.A

3. A×A

4. A/A

Subtopic:  Resolution of Vectors |
 80%
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A force \(\mathrm{F}\) applied at a \(30^\circ\) angle to the \(\mathrm{x }\)-axis has the following X and Y components:

1. F2, F

2. F2, 32F

3. 32F, 12F

4. F, F2

Subtopic:  Resolution of Vectors |
 79%
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A child pulls a box with a force of 200 N 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 |
 69%
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If  A=3i^+4j^ and B=7i^+24k^, then the vector having the same magnitude as that of B and parallel to A is:

1. 15i^ + 20j^

2. 75i^+245j^

3. 20i^+15j^

4. 15i^ + 20k^ 

Subtopic:  Resolution of Vectors |
 59%
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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 |
 59%
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