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Q. No.If two vectors \(\overrightarrow{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\overrightarrow{Q}=4 \hat{i}-2 \hat{j}+m \hat{k}\) are perpendicular to each other. Then, the value of \(m\) will be:
1. \(-1\)
2. \(2\)
3. \(1\)
4. \(3\)
1. \(-1\)
2. \(2\)
3. \(1\)
4. \(3\)
Subtopic: Â Vector Product |
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Level 1: 80%+
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If \(\left| \vec{A}\right|\) = \(2\) and \(\left| \vec{B}\right|\) = \(4,\) then match the relations in column-I with the angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) in column-II.
| Column-I | Column-II |
| (A) \(\left| \vec{A}\times \vec{B}\right|\) \(=0\) | (p) \(\theta=30^\circ\) |
| (B)\(\left| \vec{A}\times \vec{B}\right|\)\(=8\) | (q) \(\theta=45^\circ\) |
| (C) \(\left| \vec{A}\times \vec{B}\right|\) \(=4\) | (r) \(\theta=90^\circ\) |
| (D) \(\left| \vec{A}\times \vec{B}\right|\) \(=4\sqrt2\) | (s) \(\theta=0^\circ\) |
| 1. | \(\mathrm{A(s), B(r), C(q), D(p)}\) |
| 2. | \(\mathrm{A(s), B(p), C(r), D(q)}\) |
| 3. | \(\mathrm{A(s), B(p), C(q), D(r)}\) |
| 4. | \(\mathrm{A(s), B(r), C(p), D(q)}\) |
Subtopic: Â Vector Product |
 85%
Level 1: 80%+
Hints
Column-I shows some vector equations that match Column-II (in which the values of the angles between \(\vec A\) and \(\vec B\) are given).
Codes:
| Column-I | Column-II | ||
| (A) | \(|\vec A+\vec B|=|\vec A-\vec B|\) | (P) | \(45^\circ\) |
| (B) | \(|\vec A\times\vec B|=\vec A\cdot\vec B\) | (Q) | \(30^\circ\) |
| (C) | \(\vec A\cdot\vec B=\dfrac{AB}{2}\) | (R) | \(90^\circ\) |
| (D) | \(|\vec A\times\vec B|=\dfrac{AB}{2}\) | (S) | \(60^\circ\) |
| 1. | \(\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }\) |
| 2. | \(\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }\) |
| 3. | \(\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow S, D \rightarrow Q }\) |
| 4. | \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}\) |
Subtopic: Â Vector Product |
 84%
Level 1: 80%+
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If \(\overrightarrow A\) and \(\overrightarrow B\) are two vectors satisfying the relation \(\overrightarrow A.\overrightarrow B=|\overrightarrow A\times\overrightarrow B|.\) Then the value of \(|\overrightarrow A- \overrightarrow B |\) will be:
1. \(\sqrt{A^2+B^2-\sqrt{2} A B}\)
2. \(\sqrt{A^2+B^2}\)
3. \(\sqrt{A^2+B^2+2 A B}\)
4. \(\sqrt{A^2+B^2+\sqrt{2} A B}\)
1. \(\sqrt{A^2+B^2-\sqrt{2} A B}\)
2. \(\sqrt{A^2+B^2}\)
3. \(\sqrt{A^2+B^2+2 A B}\)
4. \(\sqrt{A^2+B^2+\sqrt{2} A B}\)
Subtopic: Â Vector Product |
 82%
Level 1: 80%+
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Q. No.
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