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Prove that for a vector veca defined by ...

Prove that for a vector `veca` defined by `veca=a_xveci+a_yvecj+a_zveck`, the scalar components are given by `a_x=veci.veca,a_y=vecj.veca` and `a_z=veck.veca`

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NN GHOSH-VECTOR AND SCALARS-All Questions
  1. Show that if vecA. (vecBxxvec c)=0, then vecA, vecB and vec c are copl...

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

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  3. Prove that for a vector veca defined by veca=axveci+ayvecj+azveck, the...

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  4. If vecb and vec c be the intersecting face-diagonals of a cube of edge...

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  5. Show that the position vector of a place on the surface of the earth w...

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  6. A man rows a boat with a speed 10 m/s along N-E direction. The shore l...

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  7. A force vecF=5veci+2vecj+veck displaces a body from a point with coord...

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  8. If the sum and difference of two vectors are at right angles, show tha...

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  9. Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2.

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  10. Show that if two vectors are equal in magnitude, their vector sum and ...

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  11. Find the area of the parallelogram whose sides are represented by 2h...

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  12. Show that (veca+vecb)xx(veca-vecb)=-2(vecaxxvecb) and use this result ...

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  13. Find the equation of a line through a point C of position vector vec c...

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  14. Find the moment of a force , vecF=3veci+2vecj acting at point vecr=vec...

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  15. If vecP+vecQ=vecR and vecP-vecQ=vecS, prove that vecR^2+vecS^2=2(vecP^...

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  16. Show that a vector remains invariant (unchanged ) under rotation of co...

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  17. Find the components of a vector vecA=2hati+3hatj along the directions ...

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  18. The force on a positively charged particle is given by vecF=qvecE+qvec...

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  19. A point P lies on a vector veca.the position vector of the point is ve...

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  20. Show that if vecu.(dvecu)/(dt)=0 the vector vecu is of constant magnit...

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