A particle moves from position null to (11i^+11j^+15k^) due to a uniform force of (4i^+j^+3k^)N. If the displacement is in m, then the work done will be: (Given: \(W=\vec{F}.\vec{S}\))

1. 100 J

2. 200 J

3. 300 J

4. 250 J

Subtopic:  Scalar Product |
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The dot product of two mutual perpendicular vector is:

1. 0

2. 1

3. 

4. None of the above

Subtopic:  Scalar Product |
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The angle between the two vectors -2i^ + 3j^ + k^ and i^ + 2j^ - 4k^ is:

1. 0°

2. 90°

3. 180°

4. 45°

Subtopic:  Scalar Product |
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If \(\vec{A} = 2\hat{i} + \hat{j} - \hat{k}\) ,  \(\vec{B} = \hat{i} + 2\hat{j} + 3\hat{k}\) , and \(\vec{C} = 6 \hat{i} - 2\hat{j} - 6\hat{k}\) , then the angle between \((\vec{A} + \vec{B})\) and \(\vec{C}\) will be

1.  30°

2.  45°

3.  60°

4.  90°

Subtopic:  Scalar Product |
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The magnitude of the resultant of two vectors of magnitude 3 units and 4 units is 1 unit. What is the value of their dot product?

1.  –12 units

2.  –7 units

3.  –1 unit

4.  0

Subtopic:  Scalar Product |
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A and B are two vectors given by A = 2i^ + 3j^ and B = i^ + j^. The component of A→   parallel to B is:

1.  122i^ - j^

2.  52i^ - j^

3.  52i^ + j^

4.  3i^ - 2j^2

Subtopic:  Scalar Product |
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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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The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

1. are not equal to each other in magnitude.

2. cannot be predicted.

3. are equal to each other.

4. are equal to each other in magnitude.

Subtopic:  Scalar Product |
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The angle which the vector A=2i^+3j^ makes with the y-axis, where i^ and j^ are unit vectors along x- and y-axis, respectively, is

1. cos-1 (3/5) 

2. cos-1 (2/3)

3. tan-1 (2/3)

4. sin-1 (2/3)

Subtopic:  Scalar Product |
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The unit vector perpendicular to vectors a=3i^+j^ and b=2i^-j^-5k^ is

1. ±(i^-3j^+k^)11

2. ±3i^+j^11

3. ±(2i^-j^-5k^)30

4. None of these

Subtopic:  Scalar Product |
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