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Q. No.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. \(0^\circ\)
1. \(90^\circ\)
2. \(45^\circ\)
3. \(180^\circ\)
4. \(0^\circ\)
Subtopic: Resultant of Vectors |
80%
Level 1: 80%+
NEET - 2016
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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 |
Subtopic: Scalar Product |
64%
Level 2: 60%+
NEET - 2016
Hints
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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. | \(t = 0\) |
Subtopic: Scalar Product |
61%
Level 2: 60%+
NEET - 2015
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If \(\vec F=2\hat i+\hat j-\hat k\) and \(\vec r=3\hat i+2\hat j-2\hat k,\) then the scalar and vector products of \(\vec F\) and \(\vec r\) have the magnitudes, respectively, as:
1. \(5, ~\sqrt3\)
2. \(4,~ \sqrt5\)
3. \(10, ~\sqrt2\)
4. \(10,~2\)
1. \(5, ~\sqrt3\)
2. \(4,~ \sqrt5\)
3. \(10, ~\sqrt2\)
4. \(10,~2\)
Subtopic: Vector Product |
75%
Level 2: 60%+
NEET - 2022
Hints
Vectors \(\vec {\mathrm{A}}, \vec{\mathrm{B}} \) and \(\vec{\mathrm{C}}\) are such that \(\vec{\mathrm{A}} \cdot \vec{\mathrm{B}}=0 \text { and } \vec{\mathrm{A}} \cdot \vec{\mathrm{C}}=0\). Then the vector parallel to \(\vec A\) is:
| 1. | \(\vec{A} \times \vec{B} \) | 2. | \(\vec{B}+\vec{C} \) |
| 3. | \(\vec{B} \times \vec{C} \) | 4. | \(\vec{B}~\text{and} ~\vec{C}\) |
Subtopic: Vector Product |
69%
Level 2: 60%+
NEET - 2013
Hints
If \(F=\alpha t^2-\beta t \) is the magnitude of the force acting on a particle at an instant \(t,\) then the time at which the force becomes constant is (where \(\alpha \) and \(\beta \) are constants):
| 1. | \(\dfrac{\beta}{\alpha}\) | 2. | \(\dfrac{\beta}{2\alpha}\) |
| 3. | \(\dfrac{2\beta}{\alpha}\) | 4. | zero |
Subtopic: Differentiation |
69%
Level 2: 60%+
NEET - 2024
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