Vector Addition

Q. what is polygon law of vector addition

Q. Establish the following vector inequalities geometrically or otherwise : (a) |a+b| < |a| + |b| (b) |a+b| > ||a| −|b|| (c) |a−b| < |a| + |b| (d) |a−b| > ||a| − |b|| When does the equality sign above apply?

Q.

Define null vector.

Q. 2. A force F=(2i+3j-5k)N acts at a point r1=(2i+4j+7k)m. The torque of the force aboit the point r2=(i+2j+3k)m is?

Q.

Two vectors having equal magnitudes of A make an angle θ with each other. Find the magnitude B of the resultant vector and the angle it makes with any one of the vectors?

1. B = A ,

2. B = 2 A cos ,

3. B = A cos ,

4. B = 2 A cos ,

Q. State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful : (a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions , (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.

Q. The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. What is the angle between the two vectors?

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q.

A particle is projected at angle $\theta$ with horizontal. Calculate the time when it is moving perpendicular to the initial direction.

1. 

2. 

3. 

4. 

Q. A man is walking at 2m/s towards South. To him, the wind appeares to blow from east. When he moves with double of the initial velocity, the direction of the wind appeares to be exactly from the South-East. Find the velocity of the wind and the direction of blowing.

Q. 54.Explain Triangle and Parallelogram Law of vector addition.

Q. The magnitude of the vector 3i + 4j is

1. 3 units
2. 4 units
3. 5 units
4. 10 units

Q. when a same force is applied on two different objects.it produces accelerations of 4m/sec2 and 6m/sec2.in these objects, if same force is applied on the combination of these objects, calculate acceleration of combination

Q.

Two forces 3N and 2 N are at an angle q such that the resultant is R. The first force is now increased to 6N and the resultant become 2R. The value of q is

1. ${30}^{\circ }$
   

2. ${60}^{\circ }$
   

3. ${90}^{\circ }$
   

4. ${120}^{\circ }$

Q. Which of the following option is correct in regard to the figure shown below?

1. $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$
2. $\overrightarrow{B}+\overrightarrow{C}=\overrightarrow{A}$
3. $\overrightarrow{C}+\overrightarrow{A}=\overrightarrow{B}$
4. $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}=0$

Q.

Following sets of three forces act on a body. Whose resultant cannot be zero

1. 10, 10, 10

2. 10, 10, 20

3. 10, 20, 23

4. 10, 20, 40

Q.

If vectors $3i+j+5k$ and $ai+bj-15k$ are collinear, then,

1. $a=3,b=1$

2. $a=9,b=1$

3. $a=3,b=3$

4. $a=9,b=3$

Q.

The sum of two forces $\overrightarrow{P}$ and $\overrightarrow{Q}$​ is $\overrightarrow{R}$ such that $\left|\overrightarrow{R}\right|=\left|\overrightarrow{P}\right|$. The angle $\theta$ (in degrees) that the resultant of $2\overrightarrow{P}$ and $\overrightarrow{Q}$​ will make with $\overrightarrow{Q}$​ is, ______.

Q.

The forces F₁, F_2, and F₃ are acting on a particle of mass m, such that F₂ and F₃ are mutually perpendicular and under the effect of F₁, F_2, and F₃ , the particle remains stationary. What will be the acceleration of the particle, if the force F₁ is removed?

1. 

2. 

3. 

4. 

Q. The maximum and minimum magnitude of the resultant of two vectors are $23$ units and $7$ units respectively. Then the magnitude of the resultant vector when they act perpendicular to each other is

1. $14$
2. $15$
3. $16$
4. $17$

Q. 6.A block of mass 200kg is moving with a velocity of 5m/s along the positive x-direction.At time t=0, when the body is at x=0, a constant force 0.4N is directed along -ve x-directon is applied on the body for 10s.What is the position x of the body at t=2.5s?

Q. The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

1. ${60}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q. 47. Two identical blocks each of mass 3kg placed on a friction less table are pushed by a force of 30N. Calculate - (a) acceleration of the system (b)force on block B by block A (c)force of block B on block A (d)net force on block A

Q.

A sting is wound around a pencil 50 times .The total width of all turns is 5cm.Find the thickness of the string

Q. Explanation of parallelogram law of vector addition.

Q.

Given two vectors a vector and b vector where b makes an angle theta with the positive direction of a as shown. Find the magnitude of the resultant according to triangle law in this case.

1. I tried and i think have the answer in the first attempt.

2. I am trying but I am stuck

3. I tried and did not get the answer initially but after a few attempts I think I have the right answer now.

4. I didn't try and don't want to do it on my own. I want to watch you doing it and spoon feed me like a baby

Q.

What is vector cross product used for?

Q.

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is

1. ${120}^{\circ }$
   
   

2. ${150}^{\circ }$
   
   

3. ${135}^{\circ }$

4. None of these

Q. The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If magnitude of $\overrightarrow{Q}$ is doubled, the new resultant is perpendicular to $\overrightarrow{P}.$ Then $|\overrightarrow{R}|$ equals

1. $|\overrightarrow{P}|$
2. $|(\overrightarrow{P}+\overrightarrow{Q})|$
3. $|\overrightarrow{Q}|$
4. $|\overrightarrow{P}-\overrightarrow{Q}|$

Q.

Which pair of the following forces will never give a resultant force of 2 N?

1. $2Nand2N$

2. $1Nand1N$

3. $1Nand3N$

4. $1Nand4N$

Q. Two forces of 10N and 8N can be applied to produce the effect of a single force of

1. 1 N
2. 8 N
3. 20 N
4. None of these