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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The component of vector A=3i^+j^+k^ along the direction of i^-j^ is:

1. 2

2. 2

3. 3

4. 3

Subtopic:  Scalar Product |
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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 |
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If A=B+C, and the magnitudes of A,B,C are 5, 4 and 3 units, respectively. Then the angle between A and C is:

1. cos-135

2. cos-145

3. sin-134

4. π2

Subtopic:  Resultant of Vectors |
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If vector A = cosωti^ + sinωtj^ and B = cosωt2i^ + sinωt2j^ are functions of time, then the value of t at which they are orthogonal to each other will be:

1. t = π2ω

2. t = πω

3. t = 0

4. t = π4ω

Subtopic:  Scalar Product |
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Component of 3i^+4j^ perpendicular to i^+j^ and in the same plane as that of 3i^+4j^ is:

1.  12j^-i^

2.  32j^-i^

3.  52j^-i^

4.  72j^-i^

Subtopic:  Scalar Product |
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At what angle must the two forces (x + y) and (x y) act so that the resultant comes out to be x2+y2 ?

1. cos-1-x2+y22(x2-y2)

2. cos-1-2(x2-y2)x2+y2

3. cos-1-x2+y2x2-y2

4. cos-1-x2-y2x2+y2

Subtopic:  Resultant of Vectors |
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For the given figure, which of the following is true?

                          

1. B = A + C

2. A = B + C

3. CA + B

4. All of these

Subtopic:  Resultant of Vectors |
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The value of the unit vector, which is perpendicular to both A = \(\hat{i} + 2\hat{j} + 3 \hat{k}\) and B = \(\hat{i} - 2\hat{j} - 3 \hat{k}\) is equal to:

1.  i^ + 2j^ + 3k^6

2.  6j^ - 4k^52

3.  6j^ + 4k^52

4.  2i^ - j^5

Subtopic:  Vector Product |
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The instantaneous velocity (defined as v=dsdt) at time t=π2 of a particle, whose position equation is given as  s(t)=12 tant2+π m, is

1. 12 m/s
2. 122 m/s
3. 6 m/s
4. \(6\sqrt2\) m/s

Subtopic:  Differentiation |
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