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Q. No.Two particles are located at equal distance from origin. The position vectors of those are represented by \(\vec {A} = 2\hat i + 3n\hat j + 2\hat k \) and \(\vec {B} = 2\hat i - 2\hat j + 4p\hat k,\) respectively. If both the vectors are at right angle to each other, the value of \(n^{-1} \) is:
| 1. | \(8\) | 2. | \(3\) |
| 3. | \(7\) | 4. | \(5\) |
Subtopic: Scalar Product |
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Level 2: 60%+
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Three vectors \(\overrightarrow{{OP}}, ~\overrightarrow{{OQ}},\) and \(\overrightarrow{{OR}},\) each of magnitude \({A},\) are positioned as shown in the figure. If the resultant of these three vectors is \({A \sqrt{ x},}\) the value of \({x}\) is:
| 1. | \(7\) | 2. | \(3\) |
| 3. | \(15\) | 4. | \(11\) |
Subtopic: Resultant of Vectors |
85%
Level 1: 80%+
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The resultant of two vectors
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(120^{\circ}\)
4. \(150^{\circ}\)
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(120^{\circ}\)
4. \(150^{\circ}\)
Subtopic: Resultant of Vectors |
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Level 3: 35%-60%
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If \(\vec a\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5 }{ 9}\right) \) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(n\) is:
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
1. \(4\)
2. \(3\)
3. \(2\)
4. \(1\)
Subtopic: Resultant of Vectors |
69%
Level 2: 60%+
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For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), ~\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k}) \) and \( \vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k}) \text {, }\) if \(\vec A.(\vec{B} \times \vec{C})=0 \) then value of \(x\) is:
1. \(7\)
2. \(3\)
3. \(6\)
4. \(4\)
1. \(7\)
2. \(3\)
3. \(6\)
4. \(4\)
Subtopic: Vector Product |
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Level 2: 60%+
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If a vector has a magnitude equal to that of \(\vec{A}=4 \hat{i}+3\hat{j}\) and is parallel to \(\vec{B}=4 \hat{i}+3\hat{j},\) then the \(x\) and \(y\) components of this vector in the first quadrant are \(x\) and \(3\) respectively. Then the value of \(x\) is:
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
Subtopic: Resultant of Vectors |
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Level 1: 80%+
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Two vectors, each of magnitude \(A,\) are inclined at an angle \( \theta \) to each other. The magnitude of their resultant vector is:
| 1. | \(A \cos ^2 \dfrac{\theta}{2}\) | 2. | \(2 A \cos \dfrac{\theta}{2}\) |
| 3. | \(2 A \cos \theta\) | 4. | \(A \cos \dfrac{\theta}{2}\) |
Subtopic: Resultant of Vectors |
84%
Level 1: 80%+
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If a body is moving with momentum \(\overrightarrow{P}=\sin (k t) \hat{i}\text-\cos( k t )\hat{j},\) then the angle between \(\overrightarrow{F}\) and \(\overrightarrow{P}\) is:
1. \(90^\circ\)
2. \(60^\circ\)
3. \(45^\circ\)
4. \(30^\circ\)
1. \(90^\circ\)
2. \(60^\circ\)
3. \(45^\circ\)
4. \(30^\circ\)
Subtopic: Scalar Product |
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Level 1: 80%+
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The angle (in degrees ) between the resultant of \(2 \overrightarrow{q}-2 \overrightarrow{p}\) and \(2 \overrightarrow{q}+2 \overrightarrow{p}\) with \(\overrightarrow{q} \) is:
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)
Subtopic: Scalar Product |
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If \(\overrightarrow{\mathbf{A}}{=}{2}\hat{i}{+}{3}\hat{j}{+}{2}\hat{k}\;{and}\;\overrightarrow{\mathbf{A}}{-}\overrightarrow{\mathbf{B}}{=}{2}\hat{j}\), then find \(\left|{\overrightarrow{B}}\right|\)
1. 3
2. \(3\sqrt{3}\)
3. 2
4. \(\sqrt{3}\)
1. 3
2. \(3\sqrt{3}\)
3. 2
4. \(\sqrt{3}\)
Subtopic: Resultant of Vectors |
75%
Level 2: 60%+
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