The scalar and vector product of two vectors, and is equal to:
1. \(-25\) &
2. \(25\) &
3. \(0\) &
4. \(-25\) &
Figure shows the orientation of two vectors \(u\) and \(v\) in the XY plane.
If \(u = a\hat i + b\hat j\) and \(v = p\hat i + q\hat j\)
Which of the following is correct?
1. | \(a\) and \(p\) are positive while \(b\) and \(q\) are negative |
2. | \(a, p,\) and \(b\) are positive while \(q\) is negative |
3. | \(a,q,\) and \(b\) are positive while \(p\) is negative |
4. | \(a, b, p,\) and \(q\) are all positive |
The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:
1. | are not equal to each other in magnitude. |
2. | cannot be predicted. |
3. | are equal to each other. |
4. | are equal to each other in magnitude. |
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
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
If for two vectors \(\overrightarrow{A}\) and \(\overrightarrow {B}\), \(\overrightarrow {A}\times \overrightarrow {B}=0\), then the vectors:
1. | are perpendicular to each other. |
2. | are parallel to each other. |
3. | act at an angle of \(60^{\circ}\). |
4. | act at an angle of \(30^{\circ}\). |
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. \(180^{\circ}, 0^{\circ}~\text{and}~90^{\circ}\)