Subtraction of a Vector

Q.

A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of earth. The change in the velocity as it travels half circle is

1. 200 km/hr

2. 150 km/hr

3. $100\sqrt{2}km/hr$

4. 0

Q.

If $\overrightarrow{B}$ is added to $\overrightarrow{A}$, the result is $6.0\hat{i}+1.0\hat{j}$.If $\overrightarrow{B}$is subtracted from $\overrightarrow{A}$, the result is $-4\hat{i}+7.0\hat{j}$. What is the magnitude of $\overrightarrow{A}$?

1. 

2. 

3. 

4. 

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.

If Sameer moves from point $A$ having position vector $3\hat{i}+2\hat{j}+5\hat{k}$ to point $B$ having position vector $6\hat{i}+3\hat{j}+7\hat{k}$, what is his displacement vector?

1. $3\hat{i}+\hat{j}+3\hat{k}$

2. $3\hat{i}+\hat{j}+2\hat{k}$

3. $3\hat{i}+\hat{j}+4\hat{k}$

4. $3\hat{i}+\hat{j}+7\hat{k}$

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. 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.

If Sameer moves from point $A$ having position vector $3\hat{i}+2\hat{j}+5\hat{k}$ to point $B$ having position vector $6\hat{i}+3\hat{j}+7\hat{k}$, what is his displacement vector?

1. $3\hat{i}+\hat{j}+3\hat{k}$

2. $3\hat{i}+\hat{j}+2\hat{k}$

3. $3\hat{i}+\hat{j}+4\hat{k}$

4. $3\hat{i}+\hat{j}+7\hat{k}$

Q. If Rohit moves along a circular path from point $A(0,0)$ as shown in the figure and reaches diametrically opposite point $B(5,0)$, what is his displacement vector? Given: radius of circle is $2.5$ unit.

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

Q. Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are in the ratio 3 : 1Which of the following relations is true

1. P =2Q
2. P =Q
3. PQ=1
4. None of these

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 ${60}^{\circ }$

Q.

A scooter going due east at $10m{s}^{-1}$ turns right through an angle of 90°. If the speed of the scooter remains unchanged in taking turn, the change is the velocity of the scooter is

1. $20.0m{s}^{-1}$ south eastern direction

2. Zero

3. $10.0m{s}^{-1}$ in southern direction

4. $14.14m{s}^{-1}$ in south-west direction

Q. If Rohit moves along a circular path from point $A(0,0)$ as shown in the figure and reaches diametrically opposite point $B(5,0)$, what is his displacement vector? Given: radius of circle is $2.5$ unit.

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

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. 117.A body travels in a straight line according to the equation x=4+3t-t^2 .The ratio of distance travelled to displacement in t=0 to t=2 sec is (a) 5/2 (b) 5/4 (c) 1 (d) 13/6

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 ${60}^{\circ }$