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. \(\left|\overrightarrow {v_1}\right|= \left|\overrightarrow {v_2}\right|\)

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 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. \(0^{\circ}\)

For the given figure, which of the following is true?

                          
1. \(\overrightarrow{B}= \overrightarrow{A}+\overrightarrow{C}\)
2. \(\overrightarrow{A}= \overrightarrow{B}+\overrightarrow{C}\)
3. \(\overrightarrow{C}= \overrightarrow{A}+\overrightarrow{B}\)
4. All of these

Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:

1. North-East

2. North-West

3. South-West

4. South-East

If \(\overrightarrow {A}= \overrightarrow{B}+ \overrightarrow{C}\) and the magnitudes of \(\overrightarrow {A}, \overrightarrow {B},\overrightarrow {C}\) are \(5,4\) and \(3\) units, respectively. Then the angle between \(\overrightarrow {A}~\text{and}~\overrightarrow{C}\)$\stackrel{}{}$is:
1. \(\cos^{-1}\left(\frac{3}{5}\right)\)
2. \(\cos^{-1}\left(\frac{4}{5}\right)\)
3. \(\sin^{-1}\left(\frac{3}{4}\right)\)
4. \(\frac{\pi}{2}\)

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. \(\overrightarrow {P}+ \overrightarrow {Q}= \widehat{P}+ \widehat{Q}\)

A block of weight \(W\) is supported by two strings inclined at \(60^{\circ}\) and \(30^{\circ}\) to the vertical. The tensions in the strings are \(T_1\) and \(T_2\) as shown. If these tensions are to be determined in terms of \(W\) using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium):

1.		2.
3.		4.

At what angle must the two forces \((x+y)\) and \((x-y)\) act so that the resultant comes out to be \(\sqrt{x^2+y^2}\)?
1. \(\cos^{-1}\left(-\frac{x^2+y^2}{2(x^2-y^2)}\right )\)
2. \(\cos^{-1}\left(-\frac{2(x^2-y^2)}{(x^2+y^2)}\right )\)
3. \(\cos^{-1}\left(-\frac{x^2+y^2}{x^2-y^2}\right )\)
4. \(\cos^{-1}\left(-\frac{x^2-y^2}{x^2+y^2}\right )\)

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