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 |
 92%
From NCERT
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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%
From NCERT
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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 |
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 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%
From NCERT
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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%
From NCERT
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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%
From NCERT
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Figure shows the orientation of two vectors u and v in the XY plane.

 If u=ai^+bj^ and v=pi^+qj^

     

Which of the following is correct?

1. a and p are positive while b and q are negative

2. a, p, and b are positive while q is negative

3. a, q, and b are positive while p is negative

4. a, b, p, and q are all positive

Subtopic:  Resolution of Vectors |
 56%
From NCERT
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A certain vector in the xy-plane has an x-component of \(4\) m and a y-component of \(10\) m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component will be: (approximately)
1. \(20\) m
2. \(7.2\) m
3. \(5.0\) m
4. \(4.5\) m
Subtopic:  Resolution of Vectors |
 52%
From NCERT
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If v1+v2=v1-v2 and v1 and v2 are non-zero vectors, then :

1. v1 is parallel to v2

2. v1v2

3. v1 and v2 are mutually perpendicular 

4. v1=v2

Subtopic:  Resultant of Vectors |
 77%
From NCERT
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