Vector Addition

Q.

Vector A has magnitude of 5 units and makes an angle of ${30}^{\circ }$ with the x-axis. Vector B has magnitude 10 units & make an angle of ${60}^{\circ }$ with the x-axis. Find $\overrightarrow{A}+\overrightarrow{B}$

1. 

2. 

3. 

4. 

Q. $\text{Statement I:}$
Two forces$(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$ where $\overrightarrow{P}\perp \overrightarrow{Q}$. when act at an angle ${\theta }_1$ to each other, the magnitude of their resultant is $\sqrt{3(P^2+Q^2)}.$ when they act an angle ${\theta }_2$, the magnitude of their resultant becomes $\sqrt{2(P^2+Q^2)}$. This is possible only when ${\theta }_1<{\theta }_2.$

$\text{Statement II:}$
In the situtation given above. ${\theta }_1={60}^o\text{and}{\theta }_2={90}^o$ In the light of the above statements choose the most appropriate answer from the options given below:

1. Both statement I and Statement II are false
2. Statement I is true but Statement II is false.
   
3. Statement i is false but Statement II is true.
4. Both $\text{Statement I}$ and $\text{Statement II}$ are true.

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 = 2 A cos ,

2. B = A ,

3. B = A cos ,

4. B = 2 A cos ,

Q.

If I have two vectors of length 3 and 4. What are the maximum and minimum possible lengths of the resultant?

1. 7 and 0

2. 7 and 1

3. 7 and -1

4. 5 and 0

Q.

Vector A has magnitude of 3 units and makes an angle of ${30}^{\circ }$ with the positive x-axis.

Vector B has magnitude of 4 units and makes an angle of ${120}^{\circ }$ with the positive x-axis.

Find the magnitude of the resultant and the angle that it makes with the positive x-axis.

$\left[ta{n}^{-1}\right(\frac{4}{3})={53}^{\circ }]$

1. Angle =

2. Angle =

3. Angle =

4. Angle =

Q.

How will you write the vector joining points P(1, 3, 2) and Q(4, 2, 1)? Also write the unit vector for $\underset{PQ}{\to }$

1. 

2. 

3. 

4. 

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.

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is 5 unit

1. 

2. 

3. 

4. 

Q.

Find the resultant of 2 vectors whose magnitude is 6 and 8 and make an angle of 90 degrees between them.

1. 12

2. 10

3. 6

4. 8

Q. If you take 3 steps towards North then 4 steps towards East.
Then Find the Resultant.

1. 5 in North East direction
2. 5 towards North
3. 5 towards South
4. 5 in North West direction