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If hat i+ hat j+ hat k,2 hat i+ 5 hat j,...

If `hat i+ hat j+ hat k`,`2 hat i+ 5 hat j`, `3 hat i+ 2 hat j- 3 hat k` and `hat i- 6 hat j- hat k ` are the position vectors of points A,B,C and D respectively, then find the angle between `vec AB` and `vec CD`. Are `vec AB` and `vec CD` collinear?

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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 .

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If vec a = 6hat i - hat j+ 2hat k and vec b =hat i- 3hat j - 2 hat k , find vec a - vec b .

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.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If vec a is any vector in space, then show that vec a= ( vec a* hat i...

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  2. If the vertices A,B,C of triangle ABC have position vectors (1,2,3), (...

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  3. If hat i+ hat j+ hat k,2 hat i+ 5 hat j, 3 hat i+ 2 hat j- 3 hat k and...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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