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If G is the centroid of triangle ABC, pr...

If G is the centroid of `triangle ABC`, prove that area `triangle AGB = 1/3 area triangle ABC`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Define the vector product of two vectors vec a and vec b. If vec a = 2...

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  2. If vec a= 2 hat i+ 5 hat j- 7 hat k, vec b= -3 hat I + 4 hat j+ hat k ...

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  3. If G is the centroid of triangle ABC, prove that area triangle AGB = ...

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  4. If D, E, f are the mid-point of the sides of triangle ABC, prove that ...

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  5. Using vectors prove that sin(alpha - beta)= sin alpha cos beta- cos al...

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  6. If vec a= 2 hat i+ 3 hat j+ 6 hat k, vec b= 3 hat i- 6 hat j+ 2 hat k ...

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

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  8. Integrate the following int xSin(2x)dx

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  9. Prove the following : vec a * (vec a xx vec b) = 0, where are vec a a...

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  10. Integrate the following int dx/(1+cosecx)

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  11. Integrate the following int dx/(1-cosecx)

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  12. Find the volume of the parallelopied whose co-terminus edges are repre...

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  13. Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + ...

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  14. Find λ such that the vectors vec v1 =2 hat i - hat j +hat k, vec v2= h...

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  15. Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 ha...

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  16. Prove that the points whose position vectors are 6 hat i - 7 hat j, 16...

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  17. Find x such that the four points A (4, 1, 2), B (5, x, 6), C (5, 1,-1)...

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  18. Find λ if the vectors vec a = hat i+3 hat j +hat k, vec b=2 hat i- hat...

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

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

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