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°
2. 45°
3. 180°
4. 0°
A particle moves from a point \(\left(\right. - 2 \hat{i} + 5 \hat{j} \left.\right)\) to \(\left(\right. 4 \hat{j} + 3 \hat{k} \left.\right)\) when a force of \(\left(\right. 4 \hat{i} + 3 \hat{j} \left.\right)\) \(\text{N}\) is applied. How much work has been done by the force?
1. | \(8\) J | 2. | \(11\) J |
3. | \(5\) J | 4. | \(2\) J |
If vectors A = cosωt + sinωt and B = (cosωt/2) + (sinωt/2) are functions of time, then the value of t at which they are orthogonal to each other
1. t=/4ω
2. t=/2ω
3. t=/ω
4. t=0
If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)
Six vectors have the directions as indicated in the figure. Which of the following statements may be true?
1.
2.
3.
4.