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Show that the area of the triangle conta...

Show that the area of the triangle contained between the `vec a and vecb` is is one half of the magnitude of `veca xx vecb`.

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To show that the area of the triangle formed by vectors **a** and **b** is half of the magnitude of the cross product of **a** and **b**, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Vectors**: Let vectors **a** and **b** originate from the same point. The triangle formed by these vectors has its vertices at the origin, the tip of vector **a**, and the tip of vector **b**. 2. **Area of the Triangle**: ...
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MODERN PUBLICATION-SYSTEMS OF PARTICLES AND ROTATIONAL MOTION-NCERT FILE ( NCERT TEXTBOOK EXERCISES )
  1. In the HCI molecule, the separation between the nuclei of the two atom...

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  2. A child is standing at one end of a long trolley moving with a speed v...

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  3. Show that the area of the triangle contained between the vec a and vec...

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  4. Show that veca.(vecbxxvec c) is equal in magnitude to the volume of th...

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  5. Find the components along the x,y,z axes of the angular momentum overs...

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  6. Two particles each of mass m and speed v, travel in opposite direction...

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  7. A non-uniform bar of weight W is suspended at rest by two strings of n...

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  8. A car weighs 1800 kg. The distance between its front and back axles is...

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  9. (a) Find the moment of inertia of a sphere about a tangent to the sphe...

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  10. Torques of equal magnitude are applied to hollow cylinder and a solid ...

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  11. A solid cylinder of mass 20 kg rotates about its axis with angular spe...

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  12. A child stands at the centre of turntable with his two arms out stretc...

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  13. A rope of negligible mass is wound round a hollow cylinder of mass 3 k...

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  14. To maintain a rotor at a uniform angular speed of 200 "rad s"^(-1), an...

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  15. From a uniform disc of radius R, a circular section of radius R//2 is ...

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  16. A metre stick is balanced on a knife edge at its centre. When two coin...

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  17. A solid sphere rolls down two different inclined planes of the same he...

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  18. A hoop of radius 2m, weight 100 kg. It rolls along horizontal floor so...

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  19. The oxygen molecule has a mass of 5.30 xx 10^(-26) kg and a moment of ...

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  20. A sphere rolls up an inclined plane whose inclination is 30^(@). At th...

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