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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366242 The angle between vectors $(\vec{A} \times \vec{B})$ and $(\vec{B} \times \vec{A})$ is

1 Zero

2

π

3

π / 4

4

π / 2

Explanation:

$\vec{A} \times \vec{B}$ and $\vec{B} \times \vec{A}$ are anti parallel to each other. So the angle will be $π$ .

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366243 If $A = 5$ units, $B = 6$ units and $| \vec{A} \times \vec{B} | = 15$ units, then what is the angle between $\vec{A}$ and $\vec{B}$ ?

1

30^{\circ}

2

60^{\circ}

3

90^{\circ}

4

120^{\circ}

Explanation:

$\sin θ = \frac{| \vec{A} \times \vec{B} |}{A B} = \frac{15}{5 \times 6} = \frac{1}{2} \Rightarrow θ = 30^{0}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366244 Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ atisfy the relation $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0.$ The vector $\vec{A}$ is parallel to

1

\vec{B}

2

\vec{C}

3

\vec{B} \times \vec{C}

4

\vec{B} + \vec{C}

Explanation:

If $\vec{A} \cdot \vec{B} = 0, \vec{A}$ is perpendicular to $\vec{B} .$
If $\vec{A} \cdot \vec{C} = 0, \vec{A}$ is perpendicular to $\vec{C} .$
So $\vec{A}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Also $\vec{B} \times \vec{C}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Hence $\vec{A}$ is parallel to $\vec{B} \times \vec{C} .$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366245 If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A},$ then the angle between $\vec{A}$ and $\vec{B}$ is

1

π / 2

2

π / 3

3

π

4

π / 4

Explanation:

$(\vec{A} \times \vec{B}) = (\vec{B} \times \vec{A})$
$\Rightarrow A B \sin θ (\hat{n}) = A B \sin θ (- \hat{n})$
$\Rightarrow \sin θ = - \sin θ \Rightarrow 2 \sin θ = 0$
$\Rightarrow \sin θ = 0, ∴ θ = 0 o r π$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366242 The angle between vectors $(\vec{A} \times \vec{B})$ and $(\vec{B} \times \vec{A})$ is

1 Zero

2

π

3

π / 4

4

π / 2

Explanation:

$\vec{A} \times \vec{B}$ and $\vec{B} \times \vec{A}$ are anti parallel to each other. So the angle will be $π$ .

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366243 If $A = 5$ units, $B = 6$ units and $| \vec{A} \times \vec{B} | = 15$ units, then what is the angle between $\vec{A}$ and $\vec{B}$ ?

1

30^{\circ}

2

60^{\circ}

3

90^{\circ}

4

120^{\circ}

Explanation:

$\sin θ = \frac{| \vec{A} \times \vec{B} |}{A B} = \frac{15}{5 \times 6} = \frac{1}{2} \Rightarrow θ = 30^{0}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366244 Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ atisfy the relation $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0.$ The vector $\vec{A}$ is parallel to

1

\vec{B}

2

\vec{C}

3

\vec{B} \times \vec{C}

4

\vec{B} + \vec{C}

Explanation:

If $\vec{A} \cdot \vec{B} = 0, \vec{A}$ is perpendicular to $\vec{B} .$
If $\vec{A} \cdot \vec{C} = 0, \vec{A}$ is perpendicular to $\vec{C} .$
So $\vec{A}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Also $\vec{B} \times \vec{C}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Hence $\vec{A}$ is parallel to $\vec{B} \times \vec{C} .$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366245 If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A},$ then the angle between $\vec{A}$ and $\vec{B}$ is

1

π / 2

2

π / 3

3

π

4

π / 4

Explanation:

$(\vec{A} \times \vec{B}) = (\vec{B} \times \vec{A})$
$\Rightarrow A B \sin θ (\hat{n}) = A B \sin θ (- \hat{n})$
$\Rightarrow \sin θ = - \sin θ \Rightarrow 2 \sin θ = 0$
$\Rightarrow \sin θ = 0, ∴ θ = 0 o r π$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366242 The angle between vectors $(\vec{A} \times \vec{B})$ and $(\vec{B} \times \vec{A})$ is

1 Zero

2

π

3

π / 4

4

π / 2

Explanation:

$\vec{A} \times \vec{B}$ and $\vec{B} \times \vec{A}$ are anti parallel to each other. So the angle will be $π$ .

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366243 If $A = 5$ units, $B = 6$ units and $| \vec{A} \times \vec{B} | = 15$ units, then what is the angle between $\vec{A}$ and $\vec{B}$ ?

1

30^{\circ}

2

60^{\circ}

3

90^{\circ}

4

120^{\circ}

Explanation:

$\sin θ = \frac{| \vec{A} \times \vec{B} |}{A B} = \frac{15}{5 \times 6} = \frac{1}{2} \Rightarrow θ = 30^{0}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366244 Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ atisfy the relation $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0.$ The vector $\vec{A}$ is parallel to

1

\vec{B}

2

\vec{C}

3

\vec{B} \times \vec{C}

4

\vec{B} + \vec{C}

Explanation:

If $\vec{A} \cdot \vec{B} = 0, \vec{A}$ is perpendicular to $\vec{B} .$
If $\vec{A} \cdot \vec{C} = 0, \vec{A}$ is perpendicular to $\vec{C} .$
So $\vec{A}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Also $\vec{B} \times \vec{C}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Hence $\vec{A}$ is parallel to $\vec{B} \times \vec{C} .$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366245 If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A},$ then the angle between $\vec{A}$ and $\vec{B}$ is

1

π / 2

2

π / 3

3

π

4

π / 4

Explanation:

$(\vec{A} \times \vec{B}) = (\vec{B} \times \vec{A})$
$\Rightarrow A B \sin θ (\hat{n}) = A B \sin θ (- \hat{n})$
$\Rightarrow \sin θ = - \sin θ \Rightarrow 2 \sin θ = 0$
$\Rightarrow \sin θ = 0, ∴ θ = 0 o r π$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366242 The angle between vectors $(\vec{A} \times \vec{B})$ and $(\vec{B} \times \vec{A})$ is

1 Zero

2

π

3

π / 4

4

π / 2

Explanation:

$\vec{A} \times \vec{B}$ and $\vec{B} \times \vec{A}$ are anti parallel to each other. So the angle will be $π$ .

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366243 If $A = 5$ units, $B = 6$ units and $| \vec{A} \times \vec{B} | = 15$ units, then what is the angle between $\vec{A}$ and $\vec{B}$ ?

1

30^{\circ}

2

60^{\circ}

3

90^{\circ}

4

120^{\circ}

Explanation:

$\sin θ = \frac{| \vec{A} \times \vec{B} |}{A B} = \frac{15}{5 \times 6} = \frac{1}{2} \Rightarrow θ = 30^{0}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366244 Three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ atisfy the relation $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0.$ The vector $\vec{A}$ is parallel to

1

\vec{B}

2

\vec{C}

3

\vec{B} \times \vec{C}

4

\vec{B} + \vec{C}

Explanation:

If $\vec{A} \cdot \vec{B} = 0, \vec{A}$ is perpendicular to $\vec{B} .$
If $\vec{A} \cdot \vec{C} = 0, \vec{A}$ is perpendicular to $\vec{C} .$
So $\vec{A}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Also $\vec{B} \times \vec{C}$ is perpendicular to both $\vec{B} a n d \vec{C} .$
Hence $\vec{A}$ is parallel to $\vec{B} \times \vec{C} .$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366245 If $\vec{A} \times \vec{B} = \vec{B} \times \vec{A},$ then the angle between $\vec{A}$ and $\vec{B}$ is

1

π / 2

2

π / 3

3

π

4

π / 4

Explanation:

$(\vec{A} \times \vec{B}) = (\vec{B} \times \vec{A})$
$\Rightarrow A B \sin θ (\hat{n}) = A B \sin θ (- \hat{n})$
$\Rightarrow \sin θ = - \sin θ \Rightarrow 2 \sin θ = 0$
$\Rightarrow \sin θ = 0, ∴ θ = 0 o r π$

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