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Prove that the points (1,1,1),(-2,4,1),(...

Prove that the points (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) taken in order ,are the vertices of a square. Find the area of square.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the magnitude and components of the vector 2(-1,0,3) + 3(1,1,2)-(...

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  2. Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertice...

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  3. Prove that the points (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) taken in o...

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  4. If the points (-1,-1,2),(2,m,5) and (3,11,6) are collinear, find the v...

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  5. Using vectors, find the value of 'k' such that the points (k,-10,3),(1...

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  6. The sides of a parallelogram represent the vectors 2 hat i- 4 hat j+ 5...

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

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  8. Prove that the points whose position vectors are hat i - hat j+ hat k,...

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  9. Prove that the vectors vec a = hat i- 2 hat j+ hat k, vec b= -2 hat i+...

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  10. Show that the points (1,1,1),(2,-1,2),(-1,2,2) and (2,2,-1) are coplan...

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  11. Show that the points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4) are ...

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  12. If vec a, vec b and vec c are non-coplanar (independent) vectors, prov...

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  13. Find vec v underset 1 * vec v underset 2 when vec v underset 1= 4 hat ...

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  14. Find vec v underset 1 * vec v underset 2 when vec v underset 1= (1,3,5...

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  15. Find the angle between the vectors: vec v underset 1= hat i-2 hat j-...

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  16. Find the angle between the vectors: vec v underset 1= (3,5,4) and ve...

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  17. Find the value of lambda so that the vectors vec a= 3 hat i + 3 hat j-...

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

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  19. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

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  20. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

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