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The position vectors of the points A, B,...

The position vectors of the points A, B, C and D are respectively `4 hat i+ 3 hat j- hat k`,`5 hat i+ hat j+ 2 hat k`, `2 hat i- 3hat k` and `4 hat i- 4 hat j+ 3 hat k`. Show that AB and CD are parallel.

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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).

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.

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 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 .

If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and vec c = 5 hat i +6 hat j -5hat k . show that vec a, vec b and vec c are coplanar.

Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

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

Find vec a* vec b if vec a=3 hat i+4 hat j-2 hat k and vec b=-2 hat i+ 2 hat j + hat k

Prove that the points whose position vectors are 6 hat i - 7 hat j, 16 hat i -29 hat j -4 hat k , 3 hat j -6 hat k and 2 hat i+5 hat j +10 hat k are coplanar.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the points of trisection of [PQ] if the position vectors of P and...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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