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 |
The component of vector \(\overrightarrow{A} = 3 \hat{i} + \hat{j} + \hat{k}\) along the direction of \(\hat{i} - \hat{j}\) is:
1. \(\sqrt{2}\)
2. \(2\)
3. \(\sqrt{3}\)
4. \(3\)
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. \(\left|\overrightarrow {v_1}\right|= \left|\overrightarrow {v_2}\right|\)
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 \(\overrightarrow {A}~\text{and}~\overrightarrow{C}\)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 vector \(\overrightarrow{A} = \cos \omega t \hat{i} + \sin \omega t \hat{j}\) and \(\overrightarrow{B} =\cos \frac{\omega t}{2} \hat{i} + \sin \frac{\omega t}{2} \hat{j}\) are functions of time, then the value of \(t\) at which they are orthogonal to each other will be:
1. \(t = \frac{\pi}{2\omega}\)
2. \(t = \frac{\pi}{\omega}\)
3. \(t=0\)
4. \(t = \frac{\pi}{4\omega}\)
Component of perpendicular to and in the same plane as that of is:
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
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. \(\cos^{-1}\left(-\frac{x^2-y^2}{x^2+y^2}\right )\)
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
The value of the unit vector, which is perpendicular to both \(A=\hat{i} + 2\hat{j} + 3 \hat{k}\) and \(B= \hat{i} - 2\hat{j} - 3 \hat{k}\) :
1. \(\frac{\hat{i} + 2 \hat{j} + 3 \hat{k}}{6}\)
2. \(\frac{6\hat{j} -4 \hat{k}}{\sqrt{52}}\)
3. \(\frac{6\hat{j} +4 \hat{k}}{\sqrt{52}}\)
4. \(\frac{2\hat{i} - \hat{j}}{\sqrt{5}}\)
The instantaneous velocity (defined as ) at time of a particle, whose position equation is given as s(t)=12 tanm, is:
1. 12 m/s
2. 12 m/s
3. 6 m/s
4. \(6\sqrt2\) m/s