Which of the following option is not true, if A = 3i^ + 4j^ and B = 6i^ + 8j^, where \(\mathrm{A}\) and \(\mathrm{B}\) are the magnitudes of A and B?
1. A × B = 0

2. AB = 12

3. A·B = 48

4. \(\mathrm{A}=5\)

Subtopic:  Vector Product |
 72%
From NCERT
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The angle made by the vector A = 3i^ + 3j^ + 2k^ with y-axis is:

1.  sin-1314

2.  sin-174

3.  cos-143

4.  cos-135

Subtopic:  Scalar Product |
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In the space, if the sum of vectors of unequal magnitude is zero, then the minimum number of vectors are

(1) 2

(2) 3

(3) 4

(4) 5

Subtopic:  Resultant of Vectors |
 57%
From NCERT
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If A + B is perpendicular to A - B  , then which of the following statement is correct?

1.  A = B

2.  A  B

3.  A·B = zero

4.  A + B·A - B  0

Subtopic:  Scalar Product |
 55%
From NCERT
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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 |
 80%
From NCERT
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If a + b + c = 0; then which of the following statements is incorrect?

(1) a, b and c must each be a null vector.

(2) The magnitude of a+b equals the magnitude of c.

(3) The magnitude of ä can never be greater than the sum of the magnitudes of b and c

(4) ä must lie in the plane of b and c.

Subtopic:  Resultant of Vectors |
 60%
From NCERT
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When a force of magnitude F acts on a body of mass m the acceleration produced in the body is a. If three coplanar forces of equal magnitude F act on the same body as shown in the figure, then acceleration produced is

                                

1.  0

2.  3 +1a

3.  3 -1a

4.  3a

Subtopic:  Resultant of Vectors |
 81%
From NCERT
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Three forces each of magnitude 1 N act along with the sides AB, BC, and CD of a regular hexagon. The magnitude of their resultant is:

                                

(1) 4N 

(2) Zero

(3) 2 N

(4) 1 N

Subtopic:  Resultant 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 |
 56%
From NCERT
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If a = 2i^ + j^ and b = 3i^ + 2j^, then a × b=? 

1.  1

2.  65

3.  8

4.  4 

Subtopic:  Vector Product |
 75%
From NCERT
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