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Show that the points A,B and C whose pos...

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.

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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).

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.

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.

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+ 3 hat j + 5 hat k) , B(hat i+ 2 hat j+ 3 hat k) and C(7 hat i-hat k) are collinear.

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

Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 hat i -hat j - hat k and vec c= λ hat i +7 hat j +3 hat k are coplanar.

Show that the four points with position vectors 4hati+8 hat j +12hat k, 2 hat i+4hat j +6hat k, 3 hat i +5hat j +4hatk and 5hat i+8hat j+5hatk are coplanar.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the unit vector in the direction of 12 hat i- 5 hat k.

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  2. Find a unit vector parallel to the sum of the vector vec a= hat i+ hat...

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  3. Show that the points A,B and C whose position vectors are repectively ...

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  4. Find the unit vector in the direction of sum of vectors -2 hat i- 3 ha...

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  5. If vec AB= a underset 1 hat i+ a underset 2 hat j+ a underset hat k an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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