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

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

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IF veca and vecb re two vectors show that (vecaxxvecb)^2=a^2b^2-(veca.vecb)^2

If veca and vecb are any two vectors , then prove that |vecaxxvecb|^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2)=|{:(veca.veca,veca.vecb),(veca.vecb,vecb.vecb):}| or |vecaxxvecb|^(2)+(veca.vecb)^(2)=|veca|^(2)|vecb|^(2) (This is also known as Lagrange identily)

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|

Prove that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) also interpret this result.

Prove that: (2veca-vecb)xx (veca+2vecb)=5vecaxxvecb .

Prove that | vecaxxvecb | ^ 2 = det ((veca.veca, veca.vecb), (veca.vecb, vecb.vecb))

Prove that |veca xx vecb|^(2)=|{:(veca*veca,veca *vecb),(veca*vecb,vecb*vecb):}| .

Prove that: (veca/a^2-vecb/b^2)^2=((veca-vecb)/(ab))^2

Show that, (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) .

NN GHOSH-VECTOR AND SCALARS-All Questions
  1. Prove that for a vector veca defined by veca=axveci+ayvecj+azveck, the...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If veca=m vecb+vec c, find the scalar m.

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  20. Using vector method prove that in any triangle ABC a^2=b^2+c^2-2bc cos...

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