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

Given that $\overrightarrow{\mathrm{C} }= \overrightarrow{A } + \overrightarrow{B } \mathrm{and} \overrightarrow{\mathrm{C} }$ makes an angle $\mathrm{\alpha } \mathrm{with} \overrightarrow{\mathrm{A}} \mathrm{and} \mathrm{\beta } \mathrm{with} \overrightarrow{\mathrm{B}}$. Which of the following options is correct?

1.  $\mathrm{\alpha } \mathrm{cannot} \mathrm{be} \mathrm{less} \mathrm{then} \mathrm{\beta }$

2.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}<\mathrm{B}$

3.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}>\mathrm{B}$

4.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}=\mathrm{B}$

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 F/3. The angle between the two forces is 

(1) ${\cos }^{-1}\left(-\frac{{\displaystyle 17}}{{\displaystyle 18}}\right)$

(2) ${\cos }^{-1}\left(-\frac{{\displaystyle 1}}{{\displaystyle 3}}\right)$

(3) ${\cos }^{-1}\left(\frac{{\displaystyle 2}}{{\displaystyle 3}}\right)$

(4) ${\cos }^{-1}\left(\frac{8}{9}\right)$

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 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) $-5\sqrt{2},\pi /4$

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

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

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:

1. 90°

2. 45° 

3. 180° 

4. 0°

Six vectors $\overrightarrow{a} through \overrightarrow{f}$ have the directions as indicated in the figure. Which of the following statements may be true?

1. $\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{-f}$                       
2. $\overrightarrow{d}+\overrightarrow{c}=\overrightarrow{f}$
3. $\overrightarrow{d}+\overrightarrow{e}=\overrightarrow{f}$                       
4. $\overrightarrow{b}+\overrightarrow{e}=\overrightarrow{f}$