If the sum of two unit vectors is also a unit vector, then the magnitude of their difference and angle between the two given unit vectors is:
1. \(\sqrt{3}, 60^{\circ}\)
2. \(\sqrt{3}, 120^{\circ}\)
3. \(\sqrt{2}, 60^{\circ}\)
4. \(\sqrt{2},120^{\circ}\)

If the angle between the two forces increases, the magnitude of their resultant:

1. Decreases

2. Increases

3. Remains unchanged

4. First decreases, then increases

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

Let \(\theta\) be the angle between vectors \(\overrightarrow A\) and \(\overrightarrow {B}\). Which of the following figures correctly represents the angle \(\theta\)?

1.		2.
3.		4.

The dot product of two mutual perpendicular vector is:

1. \(0\)

2. \(1\)

3. \(\infty\)

4. None of the above

The angle between vectors $\left(\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}\right)$ and $\left(\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{A}}\right)$ is:
1. zero
2. $\mathrm{\pi }$
3. $\mathrm{\pi }/4$
4. $\mathrm{\pi }/2$

If for two vectors \(\overrightarrow{A}\) and \(\overrightarrow {B}\), \(\overrightarrow {A}\times \overrightarrow {B}=0\), then the vectors:

A particle moves from position null to \(\left(11\hat i + 11\hat j + 15\hat k \right)\) due to a uniform force of \(\left(4\hat i + \hat j + 3\hat k\right)\)N. If the displacement is in m, then the work done will be: (Given: \(W=\overrightarrow {F}.\overrightarrow {S}\))
1. \(100~\text{J}\)
2. \(200~\text{J}\)
3. \(300~\text{J}\)
4. \(250~\text{J}\)

There are two force vectors, one of \(5~\text{N}\) and the other of \(12~\text{N}\). At what angle should the two vectors be added to get the resultant vector of \(17~\text{N}, 7~\text{N},\) and \(13~\text{N}\) respectively:
1. \(0^{\circ}, 180^{\circ}~\text{and}~90^{\circ}\)
2. \(0^{\circ}, 90^{\circ}~\text{and}~180^{\circ}\)
3. \(0^{\circ}, 90^{\circ}~\text{and}~90^{\circ}\)
4. \(180^{\circ}, 0^{\circ}~\text{and}~90^{\circ}\)

If \(\overrightarrow {P}= \overrightarrow {Q}\), then which of the following is NOT correct?
1. \(\widehat{P}= \widehat{Q}\)
2. \(\left|\overrightarrow {P}\right|= \left|\overrightarrow {Q}\right|\)
3. \(P\widehat{Q}= Q\widehat{P}\)
4. \(\overrightarrow {P}+ \overrightarrow {Q}= \widehat{P}+ \widehat{Q}\)