- 1(current)
Q. No.If \(|\vec{A}|=2\) and \(|\vec{B}|=4\), 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) | \(\vec{A}.\vec{B}=0\) | (i) | \(\theta=0^{\circ}\) |
| (b) | \(\vec{A}.\vec{B}=8\) | (ii) | \(\theta=90^{\circ}\) |
| (c) | \(\vec{A}.\vec{B}=4\) | (iii) | \(\theta=180^{\circ}\) |
| (d) | \(\vec{A}.\vec{B}=-8\) | (iv) | \(\theta=60^{\circ}\) |
Choose the correct answer from the options given below:
| 1. | (a)–(iii), (b)-(ii), (c)-(i), (d)-(iv) |
| 2. | (a)–(ii), (b)-(i), (c)-(iv), (d)-(iii) |
| 3. | (a)–(ii), (b)-(iv), (c)-(iii), (d)-(i) |
| 4. | (a)–(iii), (b)-(i), (c)-(ii), (d)-(iv) |
Subtopic: Scalar Product |
87%
Level 1: 80%+
Hints
Let two vectors be given as:
\(\vec{A}=a_{1} \hat{i}+b_{1} \hat{j}+c_{1} \hat{k}\) and \(\vec{B}=a_{2} \hat{i}+b_{2} \hat{j}+c_{2} \hat{k}.\)
Which of the following expressions correctly represents the angle \(\theta\) between the two vectors?
\(\vec{A}=a_{1} \hat{i}+b_{1} \hat{j}+c_{1} \hat{k}\) and \(\vec{B}=a_{2} \hat{i}+b_{2} \hat{j}+c_{2} \hat{k}.\)
Which of the following expressions correctly represents the angle \(\theta\) between the two vectors?
| 1. | \(\theta=\cos ^{-1}\left(\dfrac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\right) \) |
| 2. | \(\theta=\sin ^{-1}\left(\dfrac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\right) \) |
| 3. | \(\theta=\cos ^{-1}\left(a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}\right) \) |
| 4. | \( \theta=\sin ^{-1}\left(a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}\right) \) |
Subtopic: Scalar Product |
84%
Level 1: 80%+
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Hints
Please attempt this question first.
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 |
71%
Level 2: 60%+
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Hints
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Q. No.
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