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If a,b and c are three non-zero vectors such that `a*(bxxc)=0` and b and c are not parallel vectors, prove that `a=lamdab+muc` where `lamda` and `mu` are scalar.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b...

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  2. For any vector vec a, prove that hat i xx (vec a xx hat i)+ hat j xx (...

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  3. If a,b and c are three non-zero vectors such that a*(bxxc)=0 and b and...

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  4. Integrate the following int xcos5xdx

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  5. What is the magnitude of a unit vector ?

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  6. If vec a = x hat i +2 hat j - z hat k and vec b= 3 hat i- y hat j+hat ...

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  7. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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  8. State whether the vectors hat i, hat j and hat k are coplanar or non-c...

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  9. Integrate the following int dx/(1-secx)

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  10. What is the cosine of the angle which the vector sqrt2 hat i+ hat j +h...

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  11. Find p if the vectors 2 hat i +3 hat j + 6 hat k and p hat i+2 hat j-...

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  12. Find λ if the vector λ (hat i+ hat j+ hat k) is a unit vector.

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  13. If vec a and vec b are non-zero vectors and the angle θ between them i...

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  14. Write a vector of magnitude 9 units in the direction vector -2hat(i)+h...

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  15. If θ is the angle between two non-zero vectors vec a and vec b , then ...

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  16. If the vectors 3hat i+2 hat j+9 hat k and hat i-2p hat j+3 hat k are p...

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  17. If for any two vectors vec a and vec b, (vec a+ vec b)^2 +(vec a - vec...

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  18. Find the angle between the vectors hat i-hat j and hat j-hat k.

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  19. If vec a* vec a =0 and vec a* vec b =0, then what can be concluded abo...

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  20. If vec (PQ) =3 hat i+3 hat j+6 hat k and Q is the point (4, 5, 6), fin...

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