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Show that the area of the triangle conta...

Show that the area of the triangle contained between the vector `overset rarr(a ) and overset rarr(b)` is one half of the magnitude of `overset rarr(a) xx overset rarr(b)`

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To show that the area of the triangle formed by vectors **a** and **b** is one half of the magnitude of **a** × **b**, we can follow these steps: ### Step 1: Understand the Cross Product The cross product of two vectors **a** and **b** is defined as: \[ \mathbf{a} \times \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \sin \theta \, \mathbf{n} \] where: ...
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Projection of overset(rarr)P on overset(rarr)Q is :

(i) State the associative and commutative laws of vector addition. (ii) For two given vectors A=hat I + 2 hat j -3hat k , overset(rarr)B=2 hati -hat j + 3 hatk find the vector sum of overset(rarr)A and overset(rarr)B also find the magnitude of (overset(rarr)A+overset(rarr)B)

Are the magnitude and direction of overset(rarr) A- overset(rarr)B same as that overset(rarr)B-overset(rarr)A ?

Let overset(rarr)C = overset(rarr)A+overset(rarr)B then :

The magnitude of the vector product of two vectors and may be : overset(rarr)A and overset(rarr)B

If overset(rarr)B=noverset(rarr)A and overset(rarr)A is antiparallel with overset(rarr)B , then n is :

what is the angle between (overset(rarr)P+overset(rarr)Q) and (overset(rarr)P+overset(rarr)Q) ?

The correct relation between linear velocity overset rarr(v) and angular velocity overset rarr(omega) of a particle is

The angle between vector (overset(rarr)Axxoverset(rarr)B) and (overset(rarr)B xx overset(rarr)A) is :

The angle between vector (overset(rarr)Axxoverset(rarr)B) and (overset(rarr)B xx overset(rarr)A) is :

NCERT ENGLISH-SYSTEMS OF PARTICLES AND ROTATIONAL MOTION-EXERCISE
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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 vector overse...

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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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  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 a turn table with his two arms outstre...

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

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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 wooden sphere rolls down two different inclined planes of the ...

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

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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 solid cylinder rolls up an inclined plane of angle of inclination 30...

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