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Q. No.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. \(\dfrac{5}{\sqrt{30}} \vec{i}-\dfrac{1}{\sqrt{30}} \vec{j}+\dfrac{2}{\sqrt{30}} \vec{k}\)
If \(\overrightarrow {A}= 2\hat i + 4\hat j- 5\hat k,\) then the direction cosines of the vector are:
(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three \(+\)ve coordinate axes.)
1. \(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}~\text{and}~\frac{-5}{\sqrt{45}}\)
2. \(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{3}{\sqrt{45}}\)
3. \(\frac{4}{\sqrt{45}}, 0~\text{and}~\frac{4}{\sqrt{45}}\)
4. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)
A force of \(20\) N acts on a particle along a direction, making an angle of \(60^\circ\) with the vertical. The component of the force along the vertical direction will be:
| 1. | \(2\) N | 2. | \(5\) N |
| 3. | \(10\) N | 4. | \(20\) N |
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
1. \(A\overrightarrow A\)
2. \(\overrightarrow A \cdot\overrightarrow A\)
3. \(\overrightarrow A \times \overrightarrow A\)
4. \(\frac{\overrightarrow A}{A}\)
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Q. No.
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