Cross Product

Q. The position of a particle is given by $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})\text{m}$ and linear momentum as $\overrightarrow{p}=(3\hat{i}+4\hat{j}-2\hat{k})\text{kg-m/s}$. The angular momentum of the particle about the origin $(0,0,0)$ is perpendicular to

1. $x-$ axis
2. $y-$ axis
3. $z-$ axis
4. $xz-$ plane

Q. A particle has an angular momentum $\overrightarrow{L}$ and a linear momentum $\overrightarrow{P}$ about a reference point $O$. If $\overrightarrow{r}$ is the position vector of particle with respect to reference point, then identify correct option.

1. $\overrightarrow{L}=\overrightarrow{P}\times \overrightarrow{r}$
2. $|\overrightarrow{L}\times \overrightarrow{P}|=LP$
3. $\overrightarrow{L}\times \overrightarrow{P}=0$
4. None of these

Q. Find the angular momentum of the particle of mass $0.05\text{kg}$, position vector $\overrightarrow{r}=(8\hat{i}+4\hat{j})\text{m}$ and moving with a velocity $2\hat{i}\text{m/s}$ about the origin.

1. $-0.4\hat{i}{\text{kg-m}}^2/\text{sec}$
2. $-0.4\hat{k}{\text{kg-m}}^2/\text{sec}$
3. $0.4\hat{k}{\text{kg-m}}^2/\text{sec}$
4. $-0.4\hat{j}{\text{kg-m}}^2/\text{sec}$

Q. A particle of mass $2\text{kg}$ is moving with a uniform speed of $10\text{m/s}$ in $x-y$ plane along the line $x=6\text{m}$. Find the magnitude of the angular momentum of the particle about the origin.

1. $0{\text{kg-m}}^2/\text{sec}$
2. $60{\text{kg-m}}^2/\text{sec}$
3. $120{\text{kg-m}}^2/\text{sec}$
4. $20{\text{kg-m}}^2/\text{sec}$

Q. The position of a particle is given by $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})\text{m}$ and linear momentum as $\overrightarrow{p}=(3\hat{i}+4\hat{j}-2\hat{k})\text{kg-m/s}$. The angular momentum of the particle about the origin $(0,0,0)$ is perpendicular to

1. $x-$ axis
2. $y-$ axis
3. $z-$ axis
4. $xz-$ plane

Q. A particle has an angular momentum $\overrightarrow{L}$ and a linear momentum $\overrightarrow{P}$ about a reference point $O$. If $\overrightarrow{r}$ is the position vector of particle with respect to reference point, then identify correct option.

1. $\overrightarrow{L}=\overrightarrow{P}\times \overrightarrow{r}$
2. $|\overrightarrow{L}\times \overrightarrow{P}|=LP$
3. $\overrightarrow{L}\times \overrightarrow{P}=0$
4. None of these

Q. The position of a particle is given by $\overrightarrow{r}=(\hat{i}+2\hat{j}-\hat{k})\text{m}$ and linear momentum as $\overrightarrow{p}=(3\hat{i}+4\hat{j}-2\hat{k})\text{kg-m/s}$. The angular momentum of the particle about the origin $(0,0,0)$ is perpendicular to

1. $x-$ axis
2. $y-$ axis
3. $z-$ axis
4. $xz-$ plane

Q. A body of mass $2\text{kg}$ is moving with constant velocity $10\text{m/s}$ on a straight line $3x+4y+5=0$. Calculate its angular momentum with respect to origin.

1. $5\text{Js}$
2. $10\text{Js}$
3. $15\text{Js}$
4. $20\text{Js}$

Q. A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through ${60}^{\circ }$. The torque required to maintain the needle in this position will be

1. $\sqrt{3}W$
2. $W$
3. $\frac{\sqrt{3}}{2}W$
4. $2W$

Q.

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}$ = $\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-3\hat{j}+\hat{k}$

1. 195 sq unit

2. $\sqrt[3]{3195}$sq unit

3. 0

4. $\sqrt{195}$sq unit

Q.

Calculate the area of the triangle determined by the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}$ and $\overrightarrow{B}=-3\hat{i}+7\hat{j}$

1. 33 sq. unit

2. 21 sq. unit

3. 0 sq. unit

4. $\frac{33}{2}$ sq. unit

Q. Given $\overrightarrow{C}=\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{D}=\overrightarrow{B}\times \overrightarrow{A}$, What is the angle between $\overrightarrow{C}and\overrightarrow{D}$?

1. zero
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q.

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. Find the value of the triple product $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{A})$.

1. $A^{2}Bsi{n}^2\theta$

2. $A^{2}Bsin\theta cos\theta$

3. $A^{2}Bco{s}^2\theta$

4. 0

Q.

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}$ = $\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-3\hat{j}+\hat{k}$

1. 195 sq unit

2. $\sqrt[3]{3195}$sq unit

3. 0

4. $\sqrt{195}$sq unit

Q.

Vectors $\overrightarrow{C}$ and $\overrightarrow{D}$ have magnitudes of 3 and 4 units respectively. What is the angle between the directions of $\overrightarrow{C}$ and $\overrightarrow{D}$ if the magnitude of vector product $\overrightarrow{C}\times \overrightarrow{D}$ is x and y respectively?

(x) 0 (y) 12 units

(i) 0 (ii)$\frac{\pi }{2}$ (iii)$\frac{\pi }{3}$ (iv) $\frac{\pi }{4}$

1. (x) - (iv); (y) - (iii)

2. (x) - (i); (y) - (ii)

3. (x) - (ii); (y) - (i)

4. (x) - (i); (y) - (iv)