Q. No.The position of a particle in a rectangular co-ordinate system is \((3, 2, 5)\). Then its position vector will be:
1. \(5\hat i + 6\hat j + 2\hat k\)
2. \(3\hat i + 2\hat j + 5\hat k\)
3. \(5\hat i + 3\hat j + 2\hat k\)
4. None of these
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A scalar quantity is one that:
| 1. | is conserved in a process. |
| 2. | will never accept negative values. |
| 3. | must be dimensionless. |
| 4. | has the same value for observers with different orientations of axes. |
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If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
| 1. | \(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\). |
| 2. | \(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\). |
| 3. | \(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions. |
| 4. | \(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\). |
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If \(\overrightarrow {A}= 2\hat i + 4\hat j- 5\hat k,\) then the direction cosines of the vector are:
(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three \(+\)ve coordinate axes.)
1. \(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}~\text{and}~\frac{-5}{\sqrt{45}}\)
2. \(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{3}{\sqrt{45}}\)
3. \(\frac{4}{\sqrt{45}}, 0~\text{and}~\frac{4}{\sqrt{45}}\)
4. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)
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A force \(F\) applied at a \(30^\circ\) angle to the \(x \)-axis has the following \(X\) and \(Y\) components:
1. \(\frac{F}{\sqrt{2}}, F\)
2. \(\frac{F}{2}, \frac{\sqrt{3}}{2}F\)
3. \(\frac{\sqrt{3}}{2}F, \frac{1}{2}F\)
4. \(F , \frac{F}{\sqrt{2}}\)
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A child pulls a box with a force of \(200~\text{N}\) at an angle of \(60^{\circ}\)
1. \(100~\text{N}, ~175~\text{N}\)
2. \(86.6~\text{N}, ~100~\text{N}\)
3. \(100~\text{N}, ~86.6~\text{N}\)
4. \(100~\text{N}, ~0~\text{N}\)
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A force is \(60^{\circ}\) inclined to the horizontal. If its rectangular component in the horizontal direction is \(50\) N, then the magnitude of the force in the vertical direction is:
| 1. | \(25\) N | 2. | \(75\) N |
| 3. | \(87\) N | 4. | \(100\) N |
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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 |
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1. \(20\) m
2. \(7.2\) m
3. \(5.0\) m
4. \(4.5\) m
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If \(\left|\overrightarrow {v_1}+\overrightarrow {v_2}\right|= \left|\overrightarrow {v_1}-\overrightarrow {v_2}\right|\) and \(\overrightarrow {v_1}\) and \(\overrightarrow {v_2}\) are non-zero vectors, then:
1. \(\overrightarrow {v_1}\) is parallel to \(\overrightarrow {v_2}\)
2. \(\overrightarrow {v_1} = \overrightarrow {v_2}\)
3. \(\overrightarrow {v_1}\) and \(\overrightarrow {v_2}\) are mutually perpendicular
4. \(\left|\overrightarrow {v_1}\right|= \left|\overrightarrow {v_2}\right|\)
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