A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

(A)  180°

(B)  90°

(C)  45°

(D)  0°

Concept Questions :-

Resultant of Vectors
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If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

1. 90°2. 45°3. 180°4. 0°

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Resultant of Vectors
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If vectors A=cosωi^+sinωj^ and B=cos ωt2i^+sin ωt2j^are functions of time, then the value of t at which they are orthogonal to each other

1. t=π4ω

2. t=π2ω

3. t=πω

4. t=0

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Scalar Product
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The angle between two vectors  and  is

1.  cos-113

2.  cos-1-13

3.  sin-1-13

4.  90°

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Scalar Product
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The distance x (in ) covered by a molecule starting from point A at time t = 0 and stopping at another point B in given by the equation The distance between A and B (in) is closed to

1.  10.7

2.  20.7

3.  40.7

4.  50.7

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Differentiation
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A curve is governed by the equation y=sinx, then what is the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region)

       

1. 1 units

2. 2 units

3. 3 units

4. 4 units

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Calculate the area of disk of radius 'a' using integration

1. πa22

2. πa2

3. 32πa2

4. 2πa2

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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. Find the velocity of the particle at time instant t.

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

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The displacement of particle is zero at t=0 and at t=t it is x. It starts moving in the x direction with velocity, which varies as v=kx, where k is constant. The velocity-

1. varies with time

2. is independent to time

3. inversely proportional to time

4. inversely proportional to acceleration

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The acceleration of a particle is given as a=3x2. At t=0, v=0, x=0, the velocity at t =2 sec will be-

1.  0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s 

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