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Show that the point A,B,C and D whose po...

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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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 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.

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.

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.

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.

Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k are collinear.

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.

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 2 hat i+ 6 hat j+ 3 hat k .

Show that the points A, B and C with position vectors, vec a= 3hat i-4 hatj -4 hat k, vec b= 2 hat i -hatj +hat k and vec c =hat i-3hat j-5 hat k , respectively, form the vertices of a right angled triangle.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find a unit vector in the direction of vec a- 2 vec b+ 3 vec c if vec ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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