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Show that |vec a|vec b + |vec b|vec a pe...

Show that `|vec a|vec b + |vec b|vec a` perpendicular to `|vec a|vec b - |vec b|vec a`, for any two non-zero vectors `vec a and vec b`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the magnitude of two vectors veca and vecb, having the same magni...

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  2. If vec a =2 hat i + 2 hat j +3 hat k, vec b=-hat i + 2 hat j +hat k t...

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  3. Show that |vec a|vec b + |vec b|vec a perpendicular to |vec a|vec b - ...

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  4. If |a|=5,|a-b|=8 and |a+b|=10, then |b| is equal to

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  5. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

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  6. If either vector veca = 0or vecb = 0, then veca cdot vecb = 0.But the...

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  7. If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,...

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  8. Show that the points A(1,2,7), B(2,6,3) and C(3,10,-1) are collinear.

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  9. Show that the points A(2 hat i - hat j + hat k), B(hat i - 3 hat j- 5 ...

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  10. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  11. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  12. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  13. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  14. Find |vec a xx vec b|, if vec a = 2hat i-5 hat j+3 hat k and vec b = h...

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  15. Find a unit vector perpendicular to each of the vectors vec a+vec b an...

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  16. If a unit vector vec a, makes angles pi/3 with hat i. pi/4 with hat j ...

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  17. Show that (a-b)xx(a+b)=2(axxb)

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  18. Find λ and μ if (2 hat i + 6 hat j+27 hat k) xx (hat i +λ hat j +μ hat...

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  19. Given that vec a* vec b=0 and vec a xx vec b= vec 0. What can you conc...

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  20. Let the vectors vec a, vec b, vec c be given as a1 hat i + a2 hat j +...

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