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If `vec a, vec b, vec c` are three vectors such that `|quad vec a|=5,|`,`quad vec b|=12` and `|quad vec c|=13` and if `vec a+ vec b+ vec c= 0`, find the value of `vec a* vec b + vec b* vec c + vec c* vec a`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
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  2. If vec c is normal to vec a and vec b, show that vec cis normal to ve...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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