Two forces, $1$ N and $2$ N, act along with the lines $x=0$ and $y=0$. The equation of the line along which the resultant lies is given by:
1. $y-2x =0$
2. $2y-x =0$
3. $y+x =0$
4. $y-x =0$

Component of $3\hat{i}+4\hat{j}$ perpendicular to $\hat{i}+\hat{j}$ and in the same plane as that of $3\hat{i}+4\hat{j}$ is:

1. $\frac{1}{2}(\hat{j}-\hat{i})$

2. $\frac{3}{2}(\hat{j}-\hat{i})$

3. $\frac{5}{2}(\hat{j}-\hat{i})$

4. $\frac{7}{2}(\hat{j}-\hat{i})$

Given that $\vec {C}= \vec{A}+\vec {B}~\text{and}~\vec{C}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec {B}$. Which of the following options is correct?
1. $\alpha$ cannot be less than $\beta$
2. $\alpha <\beta, ~\text{if}~A<B$
3. $\alpha <\beta, ~\text{if}~A>B$
4. $\alpha <\beta, ~\text{if}~A=B$

If the angle between the vector $\overrightarrow{A} and \overrightarrow{B}$ is  $\theta$, the value of the product $\left(\overrightarrow{B}\times \overrightarrow{A}\right).\overrightarrow{A}$ is equal to:

1. $B{A}^2 \cos \theta$

2. $B{A}^2 \sin \theta$

3. $B{A}^2 \sin \theta \cos \theta$

4. zero

Two forces A and B have a resultant $R_1$. If B is doubled, the new resultant $R_2$ is perpendicular to A. Then

1. $R_1=A$

2. $R_1=B$

3. $R_2=A$

4. $R_2=B$

Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is 

1. 45°

2 120°

3. 150°

4. 60°

Two forces with equal magnitudes $F$ act on a body and the magnitude of the resultant force is $\frac{F}{3}$. The angle between the two forces is: 
1. $\cos^{- 1} \left(- \frac{17}{18}\right)$
2. $\cos^{- 1} \left(- \frac{1}{3}\right)$
3. $\cos^{- 1} \left(\frac{2}{3}\right)$
4. $\cos^{- 1} \left(\frac{8}{9}\right)$

Two forces are such that the sum of their magnitudes is $18~\text{N}$ and their resultant is perpendicular to the smaller force and the magnitude of the resultant is $12~\text{N}$. Then the magnitudes of the forces will be:
1. $12~\text{N}, 6~\text{N}$
2. $13~\text{N}, 5~\text{N}$
3. $10~\text{N}, 8~\text{N}$
4. $16~\text{N}, 2~\text{N}$

If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is 

1. $5\sqrt{2},\pi /3$

2. $5\sqrt{2},\pi /4$

3. $-5\sqrt{2},\pi /3$

4. $-5\sqrt{2},\pi /4$