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Calculate the product ((hat i- 2 hat j+ ...

Calculate the product `((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j- 3 hat k)) * (-3 hat i+ hat j+ 2 hat k )`.

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Evaluate the following products: (3 hat i-6 hat j+2 hat k)*(2 hat i+hat j-2 hat k) .

Show that the points A(2 hat i - hat j + hat k) , B(hat i - 3 hat j- 5 hat k ) and C(3 hat i - 4 hat j- 4 hat k) are the vertices of a right angled triangle.

Find the shortest distance (S.D.) between the lines : vec r = hat i + hat j + lambda (2 hat i- hat j + hat k) and vec r = 2 hat i + hat j- hat k + mu (3 hat i - 5 hat j + 2 hat k) .

Find the shortest distance between the lines vec r = (hat i + 2 hat j + hat k) + lambda (hat i - hat j + hat k) and vec r = ( 2 hat i - hat j - hat k) + mu ( 2 hat i + hat J + 2 hat k)

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = 2 hat i- 3 hat j + 4 hat k, vec b= hat i +2 hat j- hat k and vec c = 3 hat i -hat j +2 hat k .

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors 2 hat i+ 3 hat j + 4 hat k,hat i +2 hat j - hat k and 3 hat i -hat j +2 hat k .

Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

Find the shortest distance between the lines vec , = 2 hat i + 3 hat J + 4 hat k + lambda ( 2 hat i - hat J + hat k) and vec r = 3 hat i - 2 hat j- hat k + mu (3 hat i + 2 hat j- 4 hat k).

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

Find the unit vector in the direction of sum of vectors -2 hat i- 3 hat j+ 2 hat k , 3 hat i+ 4 hat j- 2 hat k and hat i+ 2 hat j+ 6 hat k .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the area of the triangle having the points A(1,1,1), B(1,2,3) and...

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

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  3. Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j...

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

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  5. Define the vector product of two vectors vec a and vec b. If vec a = 2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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