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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 l_(1), l_(2), l_(3) are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).

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)) .

Prove that the median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Prove that the lines joining the vertices of a tetrahedron to the centroids of the opposite faces are concurrent.

Prove analytically that the : medians of a triangle are concurrent.

Write the : Angle opposite to the side LM of triangle LMN

In an acute angle Delta ABC, let AD, BE and CF be the perpendicular from A, B and C upon the opposite sides of the triangle. (All symbols used have usual meaning in a tiangle.) The orthocentre of the Delta ABC, is the

MODERN PUBLICATION-VECTORS-Exercise
  1. If hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk ...

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  2. If vecalpha=3hati+4hatj+5hatk and vecbeta=2hati+hatj-4hatk, then expre...

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

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

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  5. If two medians of a triangle are equal, prove that the triangle is iso...

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

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  7. Prove that sum of squares of the diagonals of a parallelogram is equal...

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  8. In any DeltaABC prove by vectors that a^2=b^2+c^2-2 bc cos A.

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  9. In any DeltaABC prove by vectors that b^2=c^2+a^2-2 ca cos B.

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  10. In any triangle ABC, then by vectors, prove that : c^2=a^2+b^2-2ab cos...

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

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  12. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

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  13. In any triangle ABC, then by vectors, prove that : a=b cos C+c cos B.

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  14. Use vectors to prove that in triangleABC : b=c cos A+a cos C.

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  15. Using vector method prove that cos(A-B)=cosAcosB+sinAsinB

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

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  17. Prove that any two edges in a regular tetrahedron are perpendicular.

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  18. In each problem, find the work done by a force vecF acting on a partic...

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  19. In each problem, find the work done by a force vecF acting on a partic...

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  20. Find the work done by the force vecF=hati+2hatj+hatk acting on a parti...

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