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

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -

1. $120°$

2.  $150°$

3.  $135°$

4.  None of these

The three vectors OA, OB and OC have the same magnitude R. Then the sum of these vectors have magnitude -

1. $\mathrm{R}$

2. $\sqrt{2}\mathrm{R}$

3. $3\mathrm{R}$

4. $\left(1+\sqrt{2}\right)\mathrm{R}$

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -

(1)  40 m/s north-west

(2)  $20\sqrt{2}$ m/s north-west

(3)  40 m/s south-west

(4)  $20\sqrt{2}$ m/s south-west

Two forces, ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ are acting on a body. One force is doubled of the other force and the resultant is equal to the greater force. Then the angle between the two forces is -

(A)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(1/2\right)$

(B)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(-1/2\right)$

(C)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(-1/4\right)$

(D)  ${\cos }^{-1}<mspace\; width="1em"></mspace>\left(1/4\right)$

If the angle between vector a and b is an acute angle, then the difference a$-$b is -

(1)  the main diagonal of the parallelogram

(2)  the minor diagonal of the parallelogram

(3)  any of the above

(4)  none of the above

What displacement must be added to the displacement $25<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-6<mspace\; width="1em"></mspace>\hat{\mathrm{j}}<mspace\; width="1em"></mspace>\mathrm{m}$  to give a displacement of $7.0<mspace\; width="1em"></mspace>\mathrm{m}$ pointing in the x-direction?

(1)  $18<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-6<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$

(2)  $32<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-13<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$

(3)  $-18<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+6<mspace\; width="1em"></mspace>\hat{\mathrm{j}}<mspace\; width="1em"></mspace>$

(4)  $-25<mspace\; width="1em"></mspace>\hat{\mathrm{i}}+13<mspace\; width="1em"></mspace>\hat{\mathrm{j}}<mspace\; width="1em"></mspace>$

The value of unit vector in the direction of vector $\mathrm{A}=5<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-12<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$, is -

1. $\hat{\mathrm{i}}$

2. $\hat{\mathrm{j}}$

3. $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)/13$

4. $\left(5\hat{\mathrm{i}}-12\hat{\mathrm{j}}\right)/13$

A child pulls a box with a force of \(200~\text{N}\) at an angle of $\mathrm{}$\(60^{\circ}\) above the horizontal. Then the horizontal and vertical components of the force will be:
              

1. \(100~\text{N}, ~175~\text{N}\)
2. \(86.6~\text{N}, ~100~\text{N}\)
3. \(100~\text{N}, ~86.6~\text{N}\)
4. \(100~\text{N}, ~0~\text{N}\)