Q. No.The position of a particle in a rectangular co-ordinate system is (3,2,5)(3,2,5). Then its position vector will be:
1. 5ˆi+6ˆj+2ˆk5^i+6^j+2^k
2. 3ˆi+2ˆj+5ˆk3^i+2^j+5^k
3. 5ˆi+3ˆj+2ˆk5^i+3^j+2^k
4. None of these
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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. |
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If →a→a is a vector and xx is a non-zero scalar, then which of the following is correct?
| 1. | x→ax→a is a vector in the direction of →a→a. |
| 2. | x→ax→a is a vector collinear to →a→a. |
| 3. | x→ax→a and →a→a have independent directions. |
| 4. | x→ax→a is a vector perpendicular to →a→a. |
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If →A=2ˆi+4ˆj−5ˆk,→A=2^i+4^j−5^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√45,4√45 and −5√452√45,4√45 and −5√45
2. 1√45,2√45 and 3√451√45,2√45 and 3√45
3. 4√45,0 and 4√454√45,0 and 4√45
4. 3√45,2√45 and 5√453√45,2√45 and 5√45
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A force FF applied at a 30∘30∘ angle to the xx-axis has the following XX and YY components:
1. F√2,FF√2,F
2. F2,√32FF2,√32F
3. √32F,12F√32F,12F
4. F,F√2F,F√2
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A child pulls a box with a force of 200 N200 N at an angle of 60∘60∘
1. 100 N, 175 N100 N, 175 N
2. 86.6 N, 100 N86.6 N, 100 N
3. 100 N, 86.6 N100 N, 86.6 N
4. 100 N, 0 N100 N, 0 N
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A force is 60∘60∘ inclined to the horizontal. If its rectangular component in the horizontal direction is 5050 N, then the magnitude of the force in the vertical direction is:
| 1. | 2525 N | 2. | 7575 N |
| 3. | 8787 N | 4. | 100100 N |
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Figure shows the orientation of two vectors uu and vv in the XY plane.
If u=aˆi+bˆju=a^i+b^j and v=pˆi+qˆjv=p^i+q^j
Which of the following is correct?
| 1. | aa and pp are positive while bb and qq are negative |
| 2. | a,p,a,p, and bb are positive while qq is negative |
| 3. | a,q,a,q, and bb are positive while pp is negative |
| 4. | a,b,p,a,b,p, and qq are all positive |
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1. 2020 m
2. 7.27.2 m
3. 5.05.0 m
4. 4.54.5 m
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If |→v1+→v2|=|→v1−→v2|∣∣→v1+→v2∣∣=∣∣→v1−→v2∣∣ and →v1→v1 and →v2→v2 are non-zero vectors, then:
1. →v1→v1 is parallel to →v2→v2
2. →v1=→v2→v1=→v2
3. →v1→v1 and →v2→v2 are mutually perpendicular
4. |→v1|=|→v2|∣∣→v1∣∣=∣∣→v2∣∣
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