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In a triangle OAB, angle AOB = 90^ @. If...

In a triangle OAB, `angle AOB = 90^ @`. If P and Q are the points of trisection of AB, prove that` OP^2 + OQ^2= 5/9 AB^2`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. In any triangle ABC, show that AB^(2)+AC^(2)=2(AD^(2)+BD^(2)) wher...

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  2. Prove that in a right angled triangle the mid-point of the hypotenuse ...

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  3. In a triangle OAB, angle AOB = 90^ @. If P and Q are the points of tri...

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  4. Which of the following statements are True or False : If the diagonals...

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  5. Prove that the quadrilateral obtained by joining mid-points of adjacen...

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  6. Prove that if the diagonals of a quadrilateral bisect each other at ri...

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

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

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

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

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

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

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

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

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

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  16. 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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  17. 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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  18. Evaluate the following products: (3 hat i-6 hat j+2 hat k)*(2 hat i+ha...

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

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

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