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. $-5\sqrt{2},\pi /4$

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 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°

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

If vectors A = cosωt $\hat{i}$ + sinωt $\hat{j}$ and B = (cosωt/2) $\hat{i}$ + (sinωt/2) $\hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other

1. t=$\mathrm{\pi }$/4ω
2. t=$\mathrm{\pi }$/2ω
3. t=$\mathrm{\pi }$/ω
4. t=0 

 

Six vectors $\overrightarrow a ~\text{through}~\overrightarrow f$ 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. $\overrightarrow b + \overrightarrow e = \overrightarrow f$

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. $R_2=B$