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For any two vectors vec a and vec b, pro...

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

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If A,B,C have position vectors (0,1,1),(3,1,5),(0,3,3) respectively, p...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca).

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  16. If vec a+ vec b+ vec c= 0, show that the angletheta between vec a and ...

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  17. Using vector method, prove that in a triangle, a=b cosC+ c cosB (proje...

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  18. Show that the median to the base of ann isosceles triangle is perpendi...

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  19. Prove that in a right-angled triangle, the square of the hypotenuse is...

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  20. In any triangle ABC, show that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)) wher...

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