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If |veca|=a and |vecb|=b, prove that ((v...

If `|veca|=a` and `|vecb|=b`, prove that `((veca)/(a^2)-(vecb)/(b^2))^2=((veca-vecb)/(ab))^2`.

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MODERN PUBLICATION-VECTORS-Exercise
  1. If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p n...

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  2. Let a,b and c be three non-zero vectors which are pairwise non-colline...

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  3. Let veca and vecb be two unit vectors. If the vectors : vecc=veca+2vec...

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  4. Let ABCD be a parallelogram such that AB=q, AD=p and angleBAD be an ac...

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  5. If veca and vecb are vectors such that |veca+vecb|=sqrt(29) and vecaxx...

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  6. If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj-4hatk are t...

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  7. Let vec(PR)=3hati+hatj-2hatk and vec(SQ)=hati-3hatj-4hatk determine di...

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  8. If [vecaxxvecb vecbxxvecc veccxxveca]=lambda[veca vecb vecc]^2, ...

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  9. Let veca,vecb and vecc be three non-zero vectors such that no two of t...

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  10. Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxx...

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  11. Find the values of 'x' for which x(hati+hatj+hatk) is a unit vector.

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  12. Find the angle between the vectors hati-hatj and hatj-hatk.

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  13. Find |vecaxxvecb| if veca=2hati+hatj+3hatk and vceb=3hati+5hatj-2hatk.

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  14. Show that the following vectors are collinear : 2hati-3hatj+4hatk and ...

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  15. Show that the vectors : 2hati-hatj+hatk,hati-3hatj-5hatk and 3hati-4ha...

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  16. If |veca|=a and |vecb|=b, prove that ((veca)/(a^2)-(vecb)/(b^2))^2=((v...

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  17. If vecr=xhati+yhatj+zhatk, find : (hatrxxhati)*(hatrxxhatj)+xy.

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  18. Find the value of 'lambda' such that the vectors : 3hati+lambda hatj+5...

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  19. If |veca|=3, |vecb|=4 and |vecc|=5 and each of them is perpendicular ...

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  20. Prove that : sin(A- B) = sin A cos B -cos A sin B.

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