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Prove that [vec a -vec b, vec b - vec c,...

Prove that `[vec a -vec b, vec b - vec c, vec c- vec a] =0`

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Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ , vec b+ vec c\ , vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

For any three vectors vec a,vec b and vec c , show that vec a- vec b,vec b- vec c and vec c- vec a are coplanar.

If vec a+ vec b + vec c= 0 , show that vec axxvec b= vec bxx vec c= vec cxx vec a .

If vec a , vec b , vec c are coplanar vectors, prove that |[vec a, vec b, vec c],[vec a.vec a ,vec a.vec b,vec a.vec c],[vec b.vec a, vec b.vec b, vec b.vec c]|=vec 0 .

If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b xx vec c) +vec b xx(vec c xx vec a)+ vec c xx(vec a xx vec b) = vec 0

Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .

If vec a, vec b, vec c are three vectors such that |quad vec a|=5,| , quad vec b|=12 and |quad vec c|=13 and if vec a+ vec b+ vec c= 0 , find the value of vec a* vec b + vec b* vec c + vec c* vec a .

If vec a , vec b and vec c are non-coplanar (independent) vectors, prove that the vectors vec a- 2 vec b+ 3 vec c , -2 vec a + 3 vec b- 4 vec c and vec a -vec b+ 2 vec c are also linearly independent.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b...

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  2. For any three vectors vec a,vec b and vec c , show that vec a- vec b,v...

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  3. Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

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  4. Integrate the following int (cosx)dx/(1+sin^2x)

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  5. Prove that if vec a,vec b,vec c and vec d are any four vectors, then (...

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  6. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

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  7. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

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  8. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  9. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  10. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  11. If vec α and vec β are any vectors, prove that vec β * (vec α xx vec β...

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  12. If vec a = -2hat i -2 hat j + 4 hat k, vec b=-2 hat i +4 hat j- 2 hat...

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  13. Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 ha...

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  14. If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and ...

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  15. Integrate the following int xe^(3x)dx

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  16. Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat ...

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  17. Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat ...

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  18. Prove that the four points 4 hat i +5 hat j +hat k, -(hat j+hat k) ,3...

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  19. Integrate the following int (2x+6)dx/(x^2+6x+49)

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  20. Show that the four points having position vectors 6 hat i-7 hat j, 16 ...

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