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A vector is not changed if

1. it is rotated through an arbitrary angle

2. it is multiplied by an arbitrary scalar

3. it is cross multiplied by a unit vector

4. it is slid parallel to itself

Subtopic: Resultant of Vectors |

66%

From NCERT

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Which of the sets given below may represent the magnitudes of three vectors adding to zero?

1. 2, 4, 8

2. 4, 8, 16

3. 1, 2, 1

4. 0.5, 1, 2

Subtopic: Resultant of Vectors |

74%

From NCERT

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The resultant of \(\overrightarrow A\) and \(\overrightarrow B\) makes an angle \(\alpha\) with \(\overrightarrow A\) and \(\beta\) with \(\overrightarrow B\), then:

1. \(\alpha<\beta\)

2. \(\alpha<\beta ~\text{if} ~A<B\)

3. \(\alpha<\beta ~\text{if} ~A>B\)

4. \(\alpha<\beta ~\text{if} ~A=B\)

Subtopic: Resultant of Vectors |

78%

From NCERT

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The component of a vector is

1. always less than its magnitude

2. always greater than its magnitude

3. always equal to its magnitude

4. none of these

Subtopic: Resultant of Vectors |

From NCERT

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A vector \(\overrightarrow A\) points vertically upward and \(\overrightarrow B\) points towards north. The vector product \(\overrightarrow A\times\overrightarrow B\) is:

1. | along west | 2. | along east |

3. | zero | 4. | vertically downward |

Subtopic: Vector Product |

60%

From NCERT

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A situation may be described by using different sets of coordinate axes having different orientations.
Which of the following does not depend on the orientation of the axes?

a. the value of a scalar

b. component of a vector

c. a vector

d. the magnitude of a vector

Choose the correct option:

1. (a), (b) and (c)

2. (a), (c) and (d)

3. (b), (c) and (d)

4. All of the above

Subtopic: Scalar Product |

62%

From NCERT

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Let \(\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},\) then:

1. | \(|\overrightarrow{\mathrm{C}}|\) is always greater than \(|\overrightarrow{\mathrm{A}}|\) |

2. | \(|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|\) | It is possible to have

3. | \(|\overrightarrow{\mathrm{C}}|\) is always equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\) |

4. | \(|\overrightarrow{\mathrm{C}}|\) is never equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\) |

Subtopic: Resultant of Vectors |

59%

From NCERT

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Let the angle between two nonzero vectors \(\overrightarrow A\) and \(\overrightarrow B\) be 120° and its resultant be \(\overrightarrow C\).

1. C must be equal to | A – B |

2. C must be less than | A – B |

3. C must be greater than | A – B |

4. C may be equal to | A – B |

Subtopic: Resultant of Vectors |

From NCERT

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The x-component of the resultant of several vectors

(a) is equal to the sum of the x-components of the vector

(b) may be smaller than the sum of the magnitudes of the vectors

(c) may be greater than the sum of the magnitudes of the vectors

(d) may be equal to the sum of the magnitudes of the vectors

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (a), (b) and (d)

4. (a), (c) and (d)

Subtopic: Resultant of Vectors |

54%

From NCERT

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The magnitude of the vector product of two vectors \(|\overrightarrow A|\) and \(|\overrightarrow B|\) may be

a. greater than AB

b. equal to AB

c. less than AB

d. equal to zero

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (c), (d) and (a)

4. All of the above

Subtopic: Scalar Product |

60%

From NCERT

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Hints

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