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Prove that the perpendicular from the ve...

Prove that the perpendicular from the vertices to the opposite sides (i.e. Altitudes) of a triangle concurrent.

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If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Prove that if the diagonals of a quadrilateral bisect each other at ri...

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  2. Using vector method, prove that the altitudes of a triangle are concur...

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  3. Prove that the perpendicular from the vertices to the opposite sides (...

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  4. Prove by vectors that : cos (alpha + beta) = cos alpha cos beta- sin...

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  5. Prove by vectors that : cos (alpha - beta) = cos alpha cos beta+ sin...

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  6. In each of the following , find the work done by a force vec F acting ...

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  7. In each of the following , find the work done by a force vec F acting ...

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  8. A particle acted on by two forces 4 hat i+ 3 hat j and 3 hat i+ 2 ha...

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  9. A particle is acted upon by constant forces 4hat(i)+hat(j)-3hat(k) an...

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  10. Find vec underset(1)(v)*vec underset(2)(v) if vec underset(1)(v)=3 hat...

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  11. Find vec a* vec b if vec a= 2 hat i+ hat k and vec b= hat i+hat j+hat ...

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  12. If vec a=4 hat i+3 hat j+hat k and vec b=hat i-2 hat k, find | vec a *...

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  13. Evaluate the following products: (3 hat i-6 hat j+2 hat k)*(2 hat i+ha...

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  14. Evaluate the following products: (2 hat i+3 hat j)*(-hat i+3 hat j +ha...

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  15. Evaluate the following products: (2,-1,1)*(3,4,-1).

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

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  17. If vec a=3 hat i+4 hat j and vec b=hat i-hat j+hat k, find the value o...

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  18. Find the magnitude of vec a=(hat i+3 hat j- 2 hat k)*(-hat i+3 hat k).

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  19. Given |quad vec a|=10,|quad vec b|=2 and vec a *vec b=12, find | vec a...

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  20. Define vec a*vec b where vec a and vec b are any two vectors. Find ve...

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