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Find the points of trisection of [PQ] if...

Find the points of trisection of [PQ] if the position vectors of P and Q are respectively `3 hat i+ 2 hat j- 4 hat k` and `9 hat i+ 8 hat j-10 hat k`.

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Find the angle between the vectors 3 hat i-2 hat j -6 hat k and 4 hat i-hat j-8 hat k .

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Find the angle between the vectors hat i -2 hatj +3 hat k and 3 hat i -2 hat j +hat k .

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 7 hat i+ hat j- 3 hat k .

Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

Show that the points A,B and C whose position vectors are repectively 2 hat i+ hat j- hat k , 3 hat i- 2 hat j+ hat k and hat i+ 4 hat j- 3 hat k are collinear.

Find a unit vector perpendicular to both the vectors (3 hat i + 2 hat j - hat k) and ( hat i + 2 hat j + hat k) .

Find the angle between the vectors hat i + hat j-hat k and hat i-hat j+hat k .

Show that the point A,B,C and D whose position vectors are respectively 2 hat i+ 4 hat j+ 2 hat k , hat i+ 2 hat j+ hat k , 3 hat i+ hat j- 3 hat k and 4 hat i+3 hat j - 2 hat k are the vertices of a paralleogram (use vector method).

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec AB= a underset 1 hat i+ a underset 2 hat j+ a underset hat k an...

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  2. Find a unit vector in the direction of vec a- 2 vec b+ 3 vec c if vec ...

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  3. Find the points of trisection of [PQ] if the position vectors of P and...

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  4. Show that the point A,B,C and D whose position vectors are respectivel...

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  5. The position vectors of the points A, B, C and D are respectively 4 ha...

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  6. Find the magnitude and components of the vector 2(-1,0,3) + 3(1,1,2)-(...

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

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

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

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

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

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

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

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

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

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

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

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

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