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Let veca=hati+hatj+hatk, vecb=hati-hatj+...

Let `veca=hati+hatj+hatk`, `vecb=hati-hatj+hatk` and `vecc=hati-hatj-hatk` be three vectors. A vector `vecv` in the plane of `veca` and `vecb`, whose projection on `vecc` is `1/sqrt3`, is given by :

A

1) `hati-3hatj+3hatk`

B

2) `-3hati-3hatj-hatk`

C

3) `3hati-hatj+3hatk`

D

4) `hati+3hatj-3hatk`.

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MODERN PUBLICATION-VECTORS-Exercise
  1. If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and vec c=la...

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  2. The vectors veca and vecb are not perpendicular and vecc and vecd are ...

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  3. Let veca=hati+hatj+hatk, vecb=hati-hatj+hatk and vecc=hati-hatj-hatk b...

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  4. If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p n...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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