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With usual notations, in any triangle ABC, prove the following by vector method . (i) a^(2)=b^(2)+c^(2)-2bc cos A (ii) b^(2)=c^(2)+a^(2)-2bc cosB (iii) c^(2)=a^(2)+b^(2)-2bc cosC

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

In a DeltaABC , prove by vector method b^(2)=a^(2)+c^(2)-2"ac "cosB .

Show by vector method that sin 2A=2sin A cosA .

Show by vector method that sin 2A=2sin A cosA .

Prove the following by vector method. Altitudes of a triangle are concurrent.

In a triangleABC , prove by vector method that cos2A+cos2B+cos2Cge(-3)/(2) .

In a triangleABC , prove by vector method that cos2A+cos2B+cos2Cge(-3)/(2) .

In a triangleABC , prove by vector method that cos2A+cos2B+cos2Cge(-3)/(2) .

If D,E,F are the mid-points of the sides BC,Ca and AB respectively of a triangle ABC ,prove by vector method that Area of Delta DEF=1/4 Area of Delta ABC