Subtraction of a Vector

Q.

Why is $\cos \left(0\right)=1$?

Q.

What is the angle between $\overrightarrow{P}$ and the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$

1. Zero

2. $ta{n}^{-1}\left(\frac{P}{Q}\right)$
   

3. $ta{n}^{-1}\left(\frac{Q}{P}\right)$
   

4. $ta{n}^{-1}\left(\frac{P-Q}{P+Q}\right)$

Q.

The magnitudes of vectors $\overrightarrow{A},\overrightarrow{B}and\overrightarrow{C}$ are 3, 4 and 5 units respectively. If $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$, the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

1. $\frac{\pi }{2}$
   

2. $co{s}^{-1}\left(0.6\right)$
   

3. $ta{n}^{-1}\left(\frac{7}{5}\right)$
   

4. $\frac{\pi }{4}$

Q.

The resultant of $\overrightarrow{P}$ and $\overrightarrow{Q}$ is perpendicular to $\overrightarrow{P}$. What is the angle between $\overrightarrow{P}and\overrightarrow{Q}$

1. $co{s}^{-1}\left(\frac{P}{Q}\right)$
   

2. $co{s}^{-1}\left(\frac{-P}{Q}\right)$
   

3. $si{n}^{-1}\left(\frac{P}{Q}\right)$
   

4. $si{n}^{-1}\left(\frac{-P}{Q}\right)$

Q. A person goes 10 km north and 20 km east. What will be displacement from initial point

1. 22.36 km
2. 2 km
3. 5 km
4. 20 km

Q. If $\overrightarrow{A}=2\hat{i}+9\hat{j}+4\hat{k}$ and $\overrightarrow{B}=6\hat{i}+\hat{j}-\hat{k}$, then $3\overrightarrow{A}-\overrightarrow{B}$ is

1. $13\hat{i}+\hat{j}-26\hat{k}$
2. $13(\hat{i}+\hat{j}+\hat{k})$
3. $26(\hat{i}+\hat{k})$
4. $13(2\hat{j}+\hat{k})$

Q. If Sunil moves along a rectangular path from point $A(0,0)$ as shown in the figure to point $C$ of the rectangle, what is his displacement vector. Take line $AB$ as $x$-axis and $AD$ as $y$-axis.The dimensions of the rectangle are mentioned.

1. 3$\hat{i}$+4$\hat{j}$
2. $0$
3. 4$\hat{i}$+3$\hat{j}$
4. 4$\hat{i}$+5$\hat{j}$

Q.

What is the angle between $\overrightarrow{P}$ and the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$

1. Zero

2. $ta{n}^{-1}\left(\frac{P}{Q}\right)$
   

3. $ta{n}^{-1}\left(\frac{Q}{P}\right)$
   

4. $ta{n}^{-1}\left(\frac{P-Q}{P+Q}\right)$

Q. Vector $A$ having magnitude $\sqrt{2}$ units makes an angle ${45}^{\circ }$ with horizontal and vector $B$ having magnitude $2$ units makes an angle ${30}^{\circ }$ with horizontal as shown in the figure. What is $\overrightarrow{A}-\overrightarrow{B}$?

1. $(1+\sqrt{3})\hat{i}+2\hat{j}$
2. $(1+\sqrt{3})\hat{i}-2\hat{j}$
3. $(1-\sqrt{3})\hat{i}+2\hat{j}$
4. $(1-\sqrt{3})\hat{i}$

Q. In a two dimensional motion, a particle moves from point A (position vector ${\overrightarrow{r}}_1$), to point B (position vector ${\overrightarrow{r}}_2$). If the magnitudes of these vectors are $r_1=3\text{m}$ and $r_2=4\text{m}$ and the angles they make with the x-axis are ${\theta }_1={75}^{\circ }\text{and}{\theta }_2={15}^{\circ }$, respectively, then the magnitude of the displacement vector (in $\text{m}$) is

Q.

If $|\overrightarrow{A}-\overrightarrow{B}|=|\overrightarrow{A}|=|\overrightarrow{B}|,$ the angle between \( \vec{A}\) and $\overrightarrow{B}$

1. ${60}^{\circ }$
   

2. $0^{\circ }$
   

3. ${120}^{\circ }$
   

4. ${90}^{\circ }$

Q. If $\overrightarrow{A}=2\hat{i}+9\hat{j}+4\hat{k}$ and $\overrightarrow{B}=6\hat{i}+\hat{j}-\hat{k}$, then $3\overrightarrow{A}-\overrightarrow{B}$ is

1. $13\hat{i}+\hat{j}-26\hat{k}$
2. $13(\hat{i}+\hat{j}+\hat{k})$
3. $26(\hat{i}+\hat{k})$
4. $13(2\hat{j}+\hat{k})$

Q. A person goes 10 km north and 20 km east. What will be displacement from initial point

1. 22.36 km
2. 2 km
3. 5 km
4. 20 km

Q. If Sunil moves along a rectangular path from point $A(0,0)$ as shown in the figure to point $C$ of the rectangle, what is his displacement vector. Take line $AB$ as $x$-axis and $AD$ as $y$-axis.The dimensions of the rectangle are mentioned.

1. 3$\hat{i}$+4$\hat{j}$
2. $0$
3. 4$\hat{i}$+3$\hat{j}$
4. 4$\hat{i}$+5$\hat{j}$

Q.

The resultant of $\overrightarrow{P}$ and $\overrightarrow{Q}$ is perpendicular to $\overrightarrow{P}$. What is the angle between $\overrightarrow{P}and\overrightarrow{Q}$

1. $co{s}^{-1}\left(\frac{P}{Q}\right)$
   

2. $co{s}^{-1}\left(\frac{-P}{Q}\right)$
   

3. $si{n}^{-1}\left(\frac{P}{Q}\right)$
   

4. $si{n}^{-1}\left(\frac{-P}{Q}\right)$

Q. A truck travelling due north at $50km/hr$ turns west and travels at the same speed. What is the change in velocity?

1. $50km/hr$ north-west
2. $50\sqrt{2}km/hr$ north-west
3. $50km/hr$ south-west
4. $50\sqrt{2}km/hr$ south-west

Q. If the position vectors $\overrightarrow{A},\overrightarrow{B},\overrightarrow{C},\text{and}\overrightarrow{D}$ are $\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k},\overrightarrow{B}=4\hat{i}+5\hat{j}+6\hat{k},\overrightarrow{C}=7\hat{i}+9\hat{j}+3\hat{k},$ and $\overrightarrow{D}=4\hat{i}+6\hat{j},$ then the displacement vectors $\overrightarrow{AB}\text{and}\overrightarrow{CD}$ are

1. Perpendicular
2. Parallel
3. Antiparallel
4. Inclined at an angle of ${60}^{\circ }$