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

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

The resultant of \(\vec A\) and \(\vec B\) makes an angle \(\alpha\) with \(\vec A\) and \(\beta\) with \(\vec B,\) then:
1. \(\alpha<\beta\)
2. \(\alpha<\beta ~\text{if} ~A<B\)
3. \(\alpha<\beta ~\text{if} ~A>B\)
4. \(\alpha<\beta ~\text{if} ~A=B\)

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

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

A physical situation can be described using different sets of coordinate axes with varying orientations. Which of the following quantities remain unaffected by the orientation of the coordinate system?

Choose the correct option from the given ones:

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

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 |

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)

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