Subtraction of a Vector

Q.

Find difference between the given vectors A & B.

1. 

2. none of these

3. 

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

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

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

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. Zero

2. $10.0m{s}^{-1}$ in southern direction

3. $20.0m{s}^{-1}$ south eastern direction

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

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

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

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

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

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.

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. 0

3. 150 km/hr

4. $100\sqrt{2}km/hr$

Q.

While travelling from one station to another, a car travels 75 km North, 60 km North-east and 20 km East. The minimum distance between the two stations is

1. 72 km

2. 132 km

3. 155 km

4. 112 km

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. 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. A truck travelling due north at 20 m/s turns west and travels at the same speed. The change in its velocity be

1. $20\sqrt{2}m/sN-W$
2. $40m/sN-W$
3. $40m/sS-W$
   
4. $20\sqrt{2}m/sS-W$