Vector Component

Q. The unit vector along the vector 3i + 4j is

1. i + j
2. 3i + 4j
3. 0.3i + 0.4j
4. 0.6i + 0.8j

Q. The magnitude of components of a vector $\overrightarrow{a}$ along x and y axis respectively are

1. $\text{a cos}\theta ,\text{a sin}\theta$
2. $\text{a sin}\theta ,\text{a cos}\theta$
3. $\text{a sec}\theta ,\text{a sin}\theta$
4. $\text{a tan}\theta ,\text{a cos}\theta$

Q.

A book is lying on the table. What is the angle between the action of the book on the table and reaction of table on the book?

1. Equal

2. Unequal and in same direction

3. Equal and Opposite

4. Opposite

Q.

A heavy piece of machinery is raised by sliding it a distance of d=10m along a plank oriented at an angle, $\theta ={60}^{\circ }$ as shown in figure. How far has it moved vertically and horizontally?

1. x-5m, y-8.66m

2. x- 8.66m, y- 5m

3. x - 5m, y- 9m

4. x-4.5m, y-8.66m

Q.

What is the minimum speed I need to cross the river which is flowing in the west direction at 3 Km/hr? Be aware of the crocodiles.

1. Exactly

2. Velocity just greater than

3. Velocity Just greater than

4. I don't know

Q. Two vectors acting in the opposite directions have a resultant of 10 units. If they act at right angles to each other, then the resultant is 50 units. Calculate the magnitude of two vectors.

1. $40,30$
2. $50,40$
3. $40,50$
4. $30,40$

Q. iˆ and jˆ are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors iˆ + jˆ, and iˆ − j ˆ? What are the components of a vector A= 2 iˆ + 3j ˆalong the directions of iˆ + j ˆand iˆ − jˆ? [You may use graphical method]

Q. The angle which a vector $\hat{i}-\hat{j}+\sqrt{2}\hat{k}$ makes with x-axis is

1. ${60}^o$
2. ${120}^o$
3. ${150}^o$
4. ${\tan }^{-1}(-\frac{1}{2})$

Q. The angle which a vector $\hat{i}-\hat{j}+\sqrt{2}\hat{k}$ makes with y - axis is

1. ${60}^{\circ }$
2. ${120}^{\circ }$
3. ${150}^{\circ }$
4. $ta{n}^{-1}(-\frac{1}{2})$

Q.

When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude $F=ax+b{x}^2$, where a and b are constants. The work done in stretching the upstretched rubber band by L is

1. $\frac{1}{2}(a{L}^2+b{L}^3)$

2. $\frac{1}{2}(\frac{a{L}^2}{2}+\frac{b{L}^3}{3})$

3. $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

4. $a{L}^2+b{L}^3$

Q. What is uniform motion

Q.

There is an aeroplane taking off at the airport , at say. 800 Km/ h . You are a dog. On the runway trying to chase the shadow of the Aeroplane.take the time to be exactly noon SO that the shadow falls Vertically below the plane . How fast must you run to keep up with the shadow?

1. 800 km/h

2. More than 800 km/h

3. Less than 800 km/h

4. Can't say as it depends on the angle that the plane is making with the horizontal

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

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

Q. What is the minimum number of non coplanar forces required to a body in equilibrium?

Q. Find the projection of $\overrightarrow{A}=10\hat{i}+8\hat{j}-6\hat{k}$ along $\overrightarrow{r}=5\hat{i}+6\hat{j}+9\hat{k}$

1. $44\sqrt{\frac{2}{71}}$
2. $22\sqrt{\frac{2}{71}}$
3. $2.2\sqrt{2}$
4. $22\sqrt{2}$

Q.

A stone is projected from the ground with a velocity of 25 m/s. Two seconds later, it just clears a pole of 5m height. The angle of projection is

1. 30°

2. 45°

3. 60°

4. 75°

Q. A force F is acting on a body and its component along x-axis is 60 N. The Force F is inclined at an angle ${30}^{\circ }$ as shown. Determine F.

1. $F=30\sqrt{3}N$
2. $F=40\sqrt{3}N$
3. $F=50\sqrt{3}N$
4. $F=60\sqrt{3}N$

Q.

A force of 5 N acts on a particle along a direction making an angle of
${60}^{\circ }$ with vertical. Its vertical component be

1. 10 N

2. 3 N

3. 4 N

4. 2.5 N

Q. Three forces $\overrightarrow{F_1}$, $\overrightarrow{F_2}$ and $\overrightarrow{F_3}$ act on a body. $\overrightarrow{F_1}$ acts vertically downwards with magnitude $\sqrt{3}\text{N}$ , $\overrightarrow{F_2}$ acts horizontally leftwards with magnitude $1\text{N}$ and $\overrightarrow{F_3}$ acts at an angle $\theta$ with horizontal as shown in the figure. Find the magnitude of $\overrightarrow{F_3}$ and $\theta$ for the body to remain in equilibrium.

1. $2\text{N}$, ${30}^{\circ }$
2. $2\text{N}$, ${60}^{\circ }$
3. $1\text{N}$, ${30}^{\circ }$
4. $1\text{N}$, ${60}^{\circ }$

Q. The angle between the vector $2\hat{i}+4\hat{k}$ and the $Y$- axis is

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$
4. ${180}^{\circ }$

Q.

If $|\overrightarrow{A}\times \overrightarrow{B}|$ = $\sqrt{3}\overrightarrow{A}.\overrightarrow{B}$, then the value of $|\overrightarrow{A}+\overrightarrow{B}|$ is

1. A + B

2. 

3. 

4. 

Q. The forces P, Q & R are acting at a point in a plane. The angle between P & Q, Q & R are 150 degree and 120 degree respectively. Then for equilibrium, forces P, Q & R are in the ratio :-

Q. If the sum of all forces is zero, what are the magnitudes of the unknown forces $x$ and $y$ ?

1. 5, 10
2. 10, 5
3. 4, 6
4. 6, 4

Q. For component of vector $\overrightarrow{P}=\hat{i}+2\hat{j}-3\hat{k}$ values are in column - II, then the correct match is:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{a)}& \text{X-axis}& \text{p)}& 1\\ \text{b)}& \text{Along vector}& \text{q)}& \sqrt{14}\\ & \overrightarrow{q}=\hat{i}+2\hat{j}+\frac{5}{3}\hat{k}& & \\ \text{c)}& \text{Along vector}& \text{r)}& 0\\ & \overrightarrow{r}=2\hat{i}+4\hat{j}-6\hat{k}& & \\ \text{d)}& \text{Along vector}& \text{s)}& \sqrt{7}\\ & \overrightarrow{s}=\frac{\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{14}}& & \end{array}$

1. $a\to s,b\to q,c\to r,d\to q$
2. $a\to p,b\to r,c\to q,d\to q$
3. $a\to p,b\to r,c\to s,d\to q$
4. $a\to p,b\to q,c\to r,d\to s$

Q.

A car is moving in direction $\overrightarrow{r}=-4\hat{i}+3\hat{j}$ with a speed of 10m/s. Write velocity vector of car in vector notation.

1. $-4\hat{i}+3\hat{j}m/s$

2. $-5\hat{i}+8\hat{j}m/s$

3. $-8\hat{i}+6\hat{j}m/s$

4. $-6\hat{i}+8\hat{j}m/s$

Q. $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors given by $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+\hat{j}$. The magnitude of the component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is

1. $\frac{5}{\sqrt{2}}$
2. $\frac{3}{\sqrt{2}}$
3. $\frac{7}{\sqrt{2}}$
4. $\frac{1}{\sqrt{2}}$

Q. A force F is acting on a body and its component along x-axis is 60 N. The Force F is inclined at an angle ${30}^{\circ }$ as shown. Determine F.

1. $F=30\sqrt{3}N$
2. $F=40\sqrt{3}N$
3. $F=50\sqrt{3}N$
4. $F=60\sqrt{3}N$

Q. If $\overrightarrow{A}=4\hat{i}-2\hat{j}+6\hat{k}$ and $\overrightarrow{B}=\hat{i}-2\hat{j}-3\hat{k}$ the angle which $\overrightarrow{A}-\overrightarrow{B}$ makes with x-axis is

1. ${\cos }^{-1}\left(\frac{1}{10}\right)$
2. ${\cos }^{-1}\left(\frac{2}{\sqrt{10}}\right)$
3. ${\cos }^{-1}\left(\frac{1}{\sqrt{10}}\right)$
4. ${\cos }^{-1}\left(\frac{1}{5}\right)$

Q.

Find component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$ A||B and in perpendicular direction of $\overrightarrow{B}$ $A\perp B$.

1. A||B = 5; $A\perp B=5\sqrt{3}$

2. A||B = $5\sqrt{3};A\perp B=5$

3. A||B = -5; $A\perp B=5\sqrt{3}$

4. A||B = $5\sqrt{3};A\perp B=-5$

Q. A block of weight $W$ is kept on an inclined surface whose angle of inclination is $\theta$ with horizontal. The component of weight perpendicular to the incline is

1. $W$
2. $W\cos \theta$
3. $W\sin \theta$
4. $W\tan \theta$