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Q. No.What will be the unit vector in the direction of \(\vec{A}=5 \vec{i}+\vec{j}-2 \vec{k} \text{?}\)
1. \(\dfrac{5}{\sqrt{30}} \vec{i}+\dfrac{1}{\sqrt{30}} \vec{j}+\dfrac{2}{\sqrt{30}} \vec{k}\)
2. \(\dfrac{5}{\sqrt{30}} \vec{i}+\dfrac{1}{\sqrt{30}} \vec{j}-\dfrac{2}{\sqrt{30}} \vec{k}\)
3. \(\dfrac{5}{\sqrt{30}} \vec{i}-\dfrac{1}{\sqrt{30}} \vec{j}-\dfrac{2}{\sqrt{30}} \vec{k}\)
4. \(\dfrac{5}{\sqrt{30}} \vec{i}-\dfrac{1}{\sqrt{30}} \vec{j}+\dfrac{2}{\sqrt{30}} \vec{k}\)
1. \(\dfrac{5}{\sqrt{30}} \vec{i}+\dfrac{1}{\sqrt{30}} \vec{j}+\dfrac{2}{\sqrt{30}} \vec{k}\)
2. \(\dfrac{5}{\sqrt{30}} \vec{i}+\dfrac{1}{\sqrt{30}} \vec{j}-\dfrac{2}{\sqrt{30}} \vec{k}\)
3. \(\dfrac{5}{\sqrt{30}} \vec{i}-\dfrac{1}{\sqrt{30}} \vec{j}-\dfrac{2}{\sqrt{30}} \vec{k}\)
4. \(\dfrac{5}{\sqrt{30}} \vec{i}-\dfrac{1}{\sqrt{30}} \vec{j}+\dfrac{2}{\sqrt{30}} \vec{k}\)
Subtopic: Resolution of Vectors |
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Level 1: 80%+
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A vector has a magnitude equal to that of \(\vec{A}=4 \hat{i}+3\hat{j}\) and is parallel to \(\vec{B}=4 \hat{i}+3\hat{j}.\) If the vector lies in the first quadrant and its components along the positive \(x\)- and \(y\)-axes are \(x\) and \(3,\) respectively, the value of \(x\) is:
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
1. \(3\)
2. \(4\)
3. \(5\)
4. \(2\)
Subtopic: Resolution of Vectors |
82%
Level 1: 80%+
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A force of 5N acts on a particle along a direction making an angle of with vertical. Its vertical component will be:
1. 10 N
2. 3 N
3. 4 N
4. 2.5 N
Subtopic: Resolution of Vectors |
86%
Level 1: 80%+
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