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

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 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 

 

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, \(1\) 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. \(y-x =0\)

A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

(1)  1 N

(2)  11 N

(3)  15 N

(4)  20 N

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

(1)  2, 4, 8

(2)  4, 8, 16

(3)  1, 2, 1

(4)  0.5, 1, 2