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Q. No.A force vector \(\vec{F}\) lies in the \({xy} \)-plane and makes an angle of \(30^\circ\) with the positive \({y}\text-\)axis, as shown in the figure. If the \({y}\text-\)component of the force is given as \(2\sqrt{3}~\text{N},\) what is the corresponding \({x}\text-\)component of the force?
| 1. | \(2\sqrt{3}~\text{N} \) | 2. | \(2~\text{N}\) |
| 3. | \(3~\text{N}\) | 4. | \(3\sqrt{2}~\text{N} \) |
Subtopic: Â Resolution of Vectors |
 73%
Level 2: 60%+
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Given two vectors \(\vec{ A}=\hat i+\hat j+\hat k \) and \(\vec{ B}=\hat i+\hat j,\) the projection of \(\vec{A}\) onto \(\vec{B}\) is:
| 1. | \(2(\hat{i}+\hat{j}+\hat{k}) \) | 2. | \(\sqrt{2}(\hat{i}+\hat{j}) \) |
| 3. | \((\hat{i}+\hat{j}) \) | 4. | \(\sqrt{2}(\hat{i}+\hat{j}+\hat{k}) \) |
Subtopic: Â Resolution of Vectors |
Level 3: 35%-60%
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Two vectors \(\overrightarrow{X}\) and \(\overrightarrow{Y}\) have equal magnitude. The magnitude of \((\overrightarrow {X}\text-\overrightarrow{Y})\) is \(n\) times the magnitude of \((\overrightarrow {X}\text+\overrightarrow{Y}).\) The angle between \(\overrightarrow{X}\) and \(\overrightarrow{Y}\) is:
1. \({\cos ^{-1}\left(\dfrac{n^2+1}{n^2-1}\right)} \)
2. \({\cos ^{-1}\left(\dfrac{-n^2-1}{n^2-1}\right)} \)
3. \({\cos ^{-1}\left(\dfrac{n^2-1}{-n^2-1}\right)} \)
4. \({\cos ^{-1}\left(\dfrac{n^2+1}{-n^2-1}\right)} \)
1. \({\cos ^{-1}\left(\dfrac{n^2+1}{n^2-1}\right)} \)
2. \({\cos ^{-1}\left(\dfrac{-n^2-1}{n^2-1}\right)} \)
3. \({\cos ^{-1}\left(\dfrac{n^2-1}{-n^2-1}\right)} \)
4. \({\cos ^{-1}\left(\dfrac{n^2+1}{-n^2-1}\right)} \)
Subtopic: Â Resolution of Vectors |
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If the forces \(\overrightarrow{{OP}}, \overrightarrow{{OQ}}, \overrightarrow{{OR}}, \overrightarrow{{OS}} \text { and }\overrightarrow{{OT}}\) act simultaneously at the origin, what will be the resultant force?
\((\text{use}~ \sqrt{3}=1.7, \sqrt{2}=1.4;\) here \(\hat{i} ,\) \(\hat{{j}}\) denote unit vectors along the \( {x}, {y}\text{-axis})\)
\((\text{use}~ \sqrt{3}=1.7, \sqrt{2}=1.4;\) here \(\hat{i} ,\) \(\hat{{j}}\) denote unit vectors along the \( {x}, {y}\text{-axis})\)
| 1. | \((9.25 \hat{{i}}+5 \hat{{j}} )~\text N \) | 2. | \((3 \hat{{i}}+15 \hat{{j}} )~\text N\) |
| 3. | \((2.5 \hat{{i}}-14.5 \hat{{j}} )~\text N\) | 4. | \((-1.5 \hat{{i}}-15.5 \hat{{j}})~\text N\) |
Subtopic: Â Resolution of Vectors |
 59%
Level 3: 35%-60%
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Q. No.
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