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

A scalar quantity is one that:

If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?

A force of \(20\) N acts on a particle along a direction, making an angle of \(60^\circ\) with the vertical. The component of the force along the vertical direction will be:

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. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)

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. \(F , \frac{F}{\sqrt{2}}\)

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. \(100~\text{N}, ~0~\text{N}\)

If \(\overrightarrow A= 3\hat i + 4\hat j\) and \(\overrightarrow B = 7\hat i + 24\hat k\), then the vector having the same magnitude as that of \(\overrightarrow {B}\) and parallel to \(\overrightarrow {A}\) is:
1. \(15\hat i + 20\hat j\)
2. \(\frac{7}{5}\hat i + \frac{24}{5}\hat j\)
3. \(20\hat i + 15\hat j\)
4. \(15\hat i + 20\hat k\)

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: