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 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 |
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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 |
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A force F applied at a 30° angle to the 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 |
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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 |
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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 |
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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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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 |
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If a unit vector j^ is rotated through an angle of 45° anticlockwise, then the new vector will be:

1.  2i^ + 2j^

2.  i^ + j^

3.  12i^ + 12j^

4.  -12i^ + 12j^

Subtopic:  Resolution of Vectors |
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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.  20m
2.  7.2 m
3.  5.0 m
4.  4.5 m

Subtopic:  Resolution of Vectors |
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