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If A,B,C,D are the points with position ...

If A,B,C,D are the points with position vectors `hat i+ hat j-hat k`, `2 hat i- hat j+ 3 hat k`, `2 hat i- 3 hat k`,`3 hat i- 2 hat j+ hat k` respectively , find the projection of `vec AB` along `vec CD`.

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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.

If vec a = 7 hat i +hat j - 4 hat k and vec b=2 hat i+6 hat j +3 hat k , then find the projection of vec a on vec b .

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.

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

Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j- 3 hat k)) * (-3 hat i+ hat j+ 2 hat k ) .

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

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.

Find λ such that the vectors vec v_1 =2 hat i - hat j +hat k, vec v_2= hat i +2hat j -3 hat k and vec v_3= 3 hat i +λ hat j +5 hat k are coplanar.

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.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on ...

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  2. Find the projection of vec AB on vec PQ where P,Q,A,B are the points (...

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  3. If A,B,C,D are the points with position vectors hat i+ hat j-hat k, 2 ...

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  4. Find the projection of the vector vec a = 2 hat i+ 3 hat j+ 2 hat k on...

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  5. Find the projection of thevector hat i+ 3 hat j+ 7 hat k on the vector...

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  6. Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat ...

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  7. If A,B,C have position vectors (0,1,1),(3,1,5),(0,3,3) respectively, p...

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  8. Prove Cauchy- Schwarz inequality |quad vec a* vec b|<|quad vec a||quad...

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  9. For any two vectors vec a and vec b, prove that (vec a* vec b)^ 2 le |...

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  10. If |quad vec a|=1, |quad vec b|=1 and |quad vec a+ vec b|=1, prove tha...

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  11. If |quad vec a+ vec b|=|quad vec a- vec b|, prove that vec a and vec b...

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  12. If (vec a+ vec b)* (vec a- vec b)=0, show that |quad vec a|=|quad vec ...

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  13. If vec a and vec b are any two vectors, then prove that |quad vec a+ v...

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  14. Prove that two proper vectors vec a and vec b are the right angles iff...

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  15. If vec a,vec b,vec c are three non-coplanar vectors and vec d* vec a ...

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  16. Find a vector vec c such that vec c*(hat i+ hat j)= 2, vec c* (hat i- ...

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  17. Find a vector vec c such that vec c. hat i = vec c. hat j= vec c . hat...

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  18. If vec c is normal to vec a and vec b, show that vec cis normal to ve...

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  19. If vec a, vec b, vec c are three vectors such that |quad vec a|=5,|,qu...

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  20. If vec a,vec b,vec c are mutually perpendicular unit vectors , then f...

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