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Prove that the points whose position vec...

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.

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Show that the four points having position vectors 6 hat i-7 hat j, 16 hat i-19 hat j -4hat k, 3 hat j-6 hat k, 2 hat i+5 hat j +10 hat k are not 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.

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 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 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.

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.

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 vectors vec a = hat i- 2 hat j+ hat k , vec b= -2 hat i+ hat j+ hat k and vec c= hat i+ hat j-2 hat k are coplanar.

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 vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + 3hat j- 4hat k and vec c =hat i - 3 hat j+5 hat k are coplanar.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find λ such that the vectors vec v1 =2 hat i - hat j +hat k, vec v2= h...

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  2. Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 ha...

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  3. Prove that the points whose position vectors are 6 hat i - 7 hat j, 16...

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  4. Find x such that the four points A (4, 1, 2), B (5, x, 6), C (5, 1,-1)...

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  5. Find λ if the vectors vec a = hat i+3 hat j +hat k, vec b=2 hat i- hat...

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  6. Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b...

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  7. For any three vectors vec a,vec b and vec c , show that vec a- vec b,v...

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  8. Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

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  9. Integrate the following int (cosx)dx/(1+sin^2x)

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  10. Prove that if vec a,vec b,vec c and vec d are any four vectors, then (...

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  11. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

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  12. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

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  13. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  14. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  15. Find the volume of the Parallelopiped whose coterminous edges are repr...

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  16. If vec α and vec β are any vectors, prove that vec β * (vec α xx vec β...

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  17. If vec a = -2hat i -2 hat j + 4 hat k, vec b=-2 hat i +4 hat j- 2 hat...

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  18. Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 ha...

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  19. If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and ...

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  20. Integrate the following int xe^(3x)dx

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