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The sides of a parallelogram represent t...

The sides of a parallelogram represent the vectors `2 hat i- 4 hat j+ 5 hat k` and `hat i- 2 hat j-3 hat k`. Find the unit vectors parallel to its diagonals.

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The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hatk and hat i-2hat j-3 hatk . Find the unit vector Parallel to its diagonal. Also, find its area.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If (vec a)^2 =(vec b)^2, is it necessary that vec a= vec b ?

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  19. Find the angles which the vector 3 hat i- 6 hat j+ 2 hat k makes the c...

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  20. If vec a and vec b are two vectors such that |quad vec a + vec b|= |qu...

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