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Prove that sum of squares of the diagona...

Prove that sum of squares of the diagonals of a parallelogram is equal to sum of squares of its sides.

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Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Prove that the diagonals of a square are equal.

Prove, by vector method, that the diagonals of a parallelogram bisect each other, conversely, if the diagonals of a quadrilateral bisect each other, it is a parallelogram.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Explain how a square is. a parallelogram

MODERN PUBLICATION-VECTORS-Exercise
  1. If two medians of a triangle are equal, prove that the triangle is iso...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find the work done in moving an object along the vector vecd=3hati+2ha...

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  18. A particle acted by constant forces 4 hat i+ hat j-3 hat k and 3 hat...

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  19. Constant forces 2hati-5hatj+6hatk and hati+2hatj-hatk act on a particl...

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  20. Forces of magnitudes 5 and 3 units acting in the directions 6hati + ...

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