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If vec a= hat i+ 2hat j- 3 hat k and vec...

If `vec a= hat i+ 2hat j- 3 hat k` and `vec b= 3 hat i- hat j+ 2 hat k`, show that the vectors `vec a+ vec b` and `vec a- vec b` are at right angles.

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If vec a=5 hat i-hat j-3 hat k and vec b=hat i+3 hat j -5 hat k , then show that the vecctors vec a+vec b and vec a-vec b are perpendicular.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If the vertices A,B,C of triangle ABC have position vectors (1,2,3), (...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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