Given below are two statements:

Assertion (A):	The graph between \(P\) and \(Q\) is a straight line when \(\frac{P}{Q}\) is constant.
Reason (R):	The straight-line graph means that \(P\) is proportional to \(Q\) or \(P\) is equal to a constant multiplied by \(Q\).

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False

Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)

The projection of a vector \(\overrightarrow r = 3\hat i + \hat j + 2\hat k\) on the \(XY\)-plane has a magnitude of:
1. \(3\)
2. \(4\)
3. \(\sqrt{14}\)
4. \(\sqrt{10}\)

The angle which the vector \(\overrightarrow{A} = 2 \hat{i} + 3 \hat{j}\) makes with the \(y\text-\)axis, where \(\hat i\) and \(\hat j\) are unit vectors along \(x\text-\) and \(y\text-\)axis, respectively, is:
1. \(\cos^{-1}\left(\frac{3}{5}\right)\)
2. \(\cos^{-1}\left(\frac{2}{3}\right)\)
3. \(\tan^{-1}\left(\frac{2}{3}\right)\)
4. \(\sin^{-1}\left(\frac{2}{3}\right)\)

The components of a vector along the \(x\) and \(y\) directions are \((n+1)\) and \(1\), respectively. If the coordinate system is rotated by an angle \(\theta\), then the components change to \(n\) and \(3\). The value of \(n\) will be:
1. \(2\)
2. \(\cos60^{\circ}\)
3. \(\sin 60^{\circ}\)
4. \(3.5\)

Given that \(\vec {C}= \vec{A}+\vec {B}~\text{and}~\vec{C}\) makes an angle $\mathrm{}$\(\alpha\) with \(\vec{A}\) and\(\beta\)with \(\vec {B}\). Which of the following options is correct?
1. \(\alpha \) cannot be less than \(\beta\)
2. \(\alpha <\beta, ~\text{if}~A<B\)
3. \(\alpha <\beta, ~\text{if}~A>B\)
4. \(\alpha <\beta, ~\text{if}~A=B\)

Two forces, \(1\) N and \(2\) N, act along with the lines \(x=0\) and \(y=0\). The equation of the line along which the resultant lies is given by:
1. \(y-2x =0\)
2. \(2y-x =0\)
3. \(y+x =0\)
4. \(y-x =0\)

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:
1. \(90^{\circ}\)
2. \(45^{\circ}\)
3. \(180^{\circ}\)
4. \(0^{\circ}\)

Six vectors \(\overrightarrow a ~\text{through}~\overrightarrow f\) have the directions as indicated in the figure. Which of the following statements may be true?

      
1. \(\overrightarrow b + \overrightarrow c = -\overrightarrow f\)
2. \(\overrightarrow d + \overrightarrow c = \overrightarrow f\)
3. \(\overrightarrow d + \overrightarrow e = \overrightarrow f\)
4. \(\overrightarrow b + \overrightarrow e = \overrightarrow f\)

If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:
1. \(-1\)
2. \(\frac{-1}{2}\)
3. \(\frac{1}{2}\) 
4. \(1\)